Yvonne Choquet-Bruhat

**Yvonne Choquet-Bruhat** ( [ivɔn ʃɔkɛ bʁy.a] i; 29 Disemba 1923 - 11 Febụwarị 2025) bụ onye France na-eme mgbakọ na mwepụ yana onye physics. O mere ihe ntinye dị mkpa na ọmụmụ nke General Relativity, site n'igosi na enwere ike itinye usoro Nhazi nke Einstein (Einstein field Equations) n'ụdị Nsogbu uru mbụ nke edere nke ọma. N'afọ 2015, akwụkwọ akụkọ Classical and Quantum Gravity depụtara akwụkwọ I bipụtara e jiri mara ya dị ka otu n'ime ihe iri na atọ 'ihe dị ịrịba ama' na ọmụmụ nke General Relativity, gafee otu narị afọ nke a mụrụ maka ya.

Choquet-Bruhat bụ nwanyị mbụ a họpụtara na French Academy of Sciences ma bụrụkwa onye isi nke Legion of Honour . 

## Mmalite Ndụ ya
A mụrụ Yvonne Bruhat na Lille na 29 Disemba 1923.  Nne ya bụ prọfesọ nkà ihe ọmụma Berthe Hubert, nna ya bụrụ ọkà n'ihe ọmụmụ physics Georges Bruhat, onye nwụrụ n'afọ 1945 n'ogige ịta ahụhụ Oranienburg-Sachsenhausen .  Nwanne ya nwoke bụ François Bruhat ghọkwara onye mgbakọ na mwepụ, na-eme ihe ntinye dị ịrịba ama na ọmụmụ nke Ìgwè algebra.

Bruhat gara ụlọ akwụkwọ sekọndrị ya na Paris wee nweta Baccalaureate ya n'afọ 1941. Ọ ritere asọmpi mba Concours Général, merie ihe nrite ọlaọcha maka physics. Site n'afọ 1943 ruo 1946 ọ gụrụ akwụkwọ na École normale supérieure de jeunes filles dị na Paris, ma site n'afọ 1946 ọ bụ onye enyemaka nkuzi n'ebe ahụ ma mee nnyocha nke André Lichnerowicz nyere ndụmọdụ ya.

## Early life
A mụrụ Yvonne Bruhat na Lille na 29 Disemba 1923.  Nne ya bụ prọfesọ nkà ihe ọmụma Berthe Hubert, nna ya bụ ọkà n'ihe ọmụmụ physics Georges Bruhat, onye nwụrụ n'afọ 1945 n'ogige ịta ahụhụ Oranienburg-Sachsenhausen .  Nwanne ya nwoke bụ François Bruhat ghọkwara onye mgbakọ na mwepụ, na-eme ihe ntinye dị ịrịba ama na ọmụmụ nke Ìgwè algebra.

Bruhat gara ụlọ akwụkwọ sekọndrị ya na Paris wee nweta Baccalaureate ya n'afọ 1941. Ọ natara asọmpi mba Concours Général, merie ihe nrite ọlaọcha maka physics. Site n'afọ 1943 ruo 1946 ọ gụrụ akwụkwọ na École normale supérieure de jeunes filles na Paris, ma site na 1946 ọ bụ onye enyemaka nkuzi n'ebe ahụ ma mee nnyocha nke André Lichnerowicz nyere ndụmọdụ ya.
## Early life

**Yvonne Choquet-Bruhat** ( [ivɔn ʃɔkɛ bʁy.a] i; 29 Disemba 1923 - 11 Febụwarị 2025) bụ onye France na-eme mgbakọ na mwepụ yana onye physics. O mere ihe ntinye dị mkpa na ọmụmụ nke General Relativity, site n'igosi na enwere ike itinye usoro Nhazi nke Einstein (Einstein field Equations) n'ụdị Nsogbu uru mbụ nke edere nke ọma. N'afọ 2015, akwụkwọ akụkọ Classical and Quantum Gravity depụtara akwụkwọ I bipụtara e jiri mara ya dị ka otu n'ime ihe iri na atọ 'ihe dị ịrịba ama' na ọmụmụ nke General Relativity, gafee otu narị afọ nke a mụrụ maka ya.

Choquet-Bruhat bụ nwanyị mbụ a họpụtara na French Academy of Sciences ma bụrụkwa onye isi nke Legion of Honour . 

## Mmalite Ndụ ya
A mụrụ Yvonne Bruhat na Lille na 29 Disemba 1923.  Nne ya bụ prọfesọ nkà ihe ọmụma Berthe Hubert, nna ya bụ ọkà n'ihe ọmụmụ physics Georges Bruhat, onye nwụrụ n'afọ 1945 n'ogige ịta ahụhụ Oranienburg-Sachsenhausen .  Nwanne ya nwoke bụ François Bruhat ghọkwara onye mgbakọ na mwepụ, na-eme ihe ntinye dị ịrịba ama na ọmụmụ nke Ìgwè algebra.

Bruhat gara ụlọ akwụkwọ sekọndrị ya na Paris wee nweta Baccalaureate ya n'afọ 1941. Ọ natara asọmpi mba Concours Général, merie ihe nrite ọlaọcha maka physics. Site n'afọ 1943 ruo 1946 ọ gụrụ akwụkwọ na École normale supérieure de jeunes filles na Paris, ma site na 1946 ọ bụ onye enyemaka nkuzi n'ebe ahụ ma mee nnyocha nke André Lichnerowicz nyere ndụmọdụ ya.

## Ọrụ ya
Site n'afọ 1949 ruo 1951 Bruhat bụụrụ onye enyemaka nnyocha na French National Centre for Scientific Research, n'ihi ya ọ natara nzere ọkankuzi ya.

N'afọ 1951, ọ ghọrọ onye nnyocha nwetarala nzere ọkankuzi na Institute for Advanced Study na Princeton, New Jersey. Onye nlekọta ọrụ ya, Jean Leray, tụrụ aro ka ọ mụọ usoro Nhazi nke Einstein (Einstein field Equations). O mekwara ọ mata Albert Einstein, onye ọ gakwuuru ugboro ole na ole n'oge ọ nọ n'ụlọ akwụkwọ ahụ.

N'afọ 1952, e nyere Bruhat na di ya ọrụ na Marseilles, na-eme ka ọ pụọ n'oge na-adịghị anya n'ụlọ akwụkwọ ahụ. N'otu afọ ahụ, o bipụtara ịdị adị na ịbụ ihe pụrụ iche nke ụ́sà maka Usoro nhazi nke Einstein, bụ ọrụ ya kachasị ewu ewu. Ọrụ ya na-egosi ezi echiche nke usoro Einstein,  wee malite ọmụmụ nke dynamics in General Relativity.

N'afọ 1958, e nyere ya Ihe nrite ọlaọcha nke CNRS .  Site n'afọ 1958 ruo 1959 ọ kụziri ihe na Mahadum Reims . N'afọ 1960, ọ ghọrọ prọfesọ na *Mahadum Pierre-et-Marie-Curie* (UPMC) dị na Paris, ma nọgide na-abụ prọfesọ ma ọ bụ prọfesọ lara ezumike nká ruo mgbe ọ lara ezumike nká n'afọ 1992.
thumb|235x235px|Choquet-Bruhat na Gustave Choquet na Mahadum California, Berkeley, n'afọ 1974.
Na Mahadum Pierre et Marie Curie, ọ gara n'ihu na-eme ihe ntinye dị ukwuu na physics mgbakọ na mwepụ, ọkachasị na General Relativity, Supergravity, nakwa non-Abelian gauge theory of the standard model. Ọrụ ya n'afọ 1981 yana Demetrios Christodoulou gosipụtara ịdị adị nke ụ́sà zuru ụwa ọnụ nke Yang-Mills, Higgs, na usoro nhazi nke spinor na 3 + 1 Dimensions. Tụkwasị na nke a, n'afọ 1984, o mere ma eleghị anya ọmụmụ ihe mbụ nke onye na-eme mgbakọ na mwepụ mere nke supergravity nwere nsonaazụ nke enwere ike ịgbatị gaa na ihe nlereanya dị mkpa ugbu a na D=11 Dimensions.

N'afọ 1978, a họpụtara Yvonne Choquet-Bruhat ka ọ bụrụ onye nnọchi anya Academy of Sciences ma na 14 Mee 1979 ọ ghọrọ nwanyị mbụ a họpụtara ka ọ bụrụ onye òtù zuru oke. Site n'afọ 1980 ruo 1983 ọ bụụrụ onye isi oche nke **' ("Komiti mba ụwa na General Relativity na Gravitation"). N'afọ 1985, a họpụtara ya gaa na American Academy of Arts and Sciences. N'afọ 1986, a họpụtara ya ka ọ kụzie nkuzi a ma ama Noether Lecture nke Association for Women in Mathematics.

=== Ihe Ntinye ya na Nnyocha teknụzụ ===
Nnyocha a ma ama nke Choquet-Bruhat na-ekwu maka ọdịdị mgbakọ na mwepụ nke usoro data mbụ nke General Relativity. Enwere ike ịkọwa nchịkọta nke nsonaazụ naanị n'ihe gbasara ihe dị iche iche dị iche iche.

* Ntọala M" style="font-style:italic;" typeof="M:Transclusion">g":{"wt":"mvar","href":"./Template:Mvar"},"params":{"1":{"wt":"M"}},"i":0}}]}' data-ve-no-generated-contents="true" id="mweg" style="font-style:italic;" typeof="mw:Transclusion">M">data mbụ bụ triplet k)"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mweQ" typeof="mw:Transclusion"> seetị data (''M'', ''g'', ''k'') nke M bụ ọnụọgụ atọ dị nro, g bụ ọnụọụọgụ Riemannian dị nro na M, na k bụ mpaghara dị nro (0,2) -tensor na M.
* Nyere data mbụ f":"./Template:Math"},"params":{"1":{"wt":"(M, g, k)"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mwgQ" typeof="mw:Transclusion">(''M'', ''g'', ''k''), **mmepe** nke (M,g, k) bụ Ụdị Lorentzian anọ (M, g) tinyere ntinye dị nro f: M → M na mpaghara vector dị nro n'akụkụ f nke mere na f *g = g na nke mere na ụdị nke abụọ nke f, n'ihe gbasara mpaghara vector e nyere, bụ k.

N'echiche a, enwere ike ile usoro data mbụ anya dị ka ntụziaka nke submanifold geometry nke embedded spacelike hypersurface dị  na Lorentzian manifold.

* Ntọala data mbụ (M, g, k) na-emezu usoro mgbochi ikuku, ma ọ bụ a na-ekwu na ọ bụ usoro data mbụ nke ikuku, ma ọ bụrụ na a na-emenụ mmusoro abụọ na-esonụ:

:: <math>\begin{align}
R_g-|k|_g^2+(\operatorname{tr}_gk)^2&=0\\
\operatorname{div}_gk-d(\operatorname{tr}_gk)&=0.
\end{align}</math>
: N'ebe a, g":{"wt":"math","href":"./Template:Math"},"params":{"1":{"wt":"Rg"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mwmQ" typeof="mw:Transclusion">''R<sub>g</sub>'' na-egosi nkwonkwo scalar nke g.

Otu n'ime nsonaazụ Choquet-Bruhat nke afọ 1952 na-ekwu ihe ndị a:

 

N'ikwu ya n'ụzọ dị nkenke, enwere ike ịchịkọta nke a dị ka ịsị na enwere oghere (M, g) nke f (M) bụ elu Cauchy. A na-akpọ mmepe dị otú ahụ mmepe ikuku zuru ụwa ọnụ. Choquet-Bruhat gosikwara na ọ bụ ihe pụrụ iche:

 

N'ụdị na-edoghị anya, nke a na-ekwu: nyere ihe ọ bụla dị ka oghere M nke Ricci-flat Lorentzian M M, geoM nke M dị nso na M bụ nke submanifold geometry nke m kpebiri n'ụzọ zuru ezu.

N'otu edemede ya na Robert Geroch dere n'afọ 1969, Choquet-Bruhat mere ka ọdịdị nke ịdị iche doo anya. Site na arụmụka peeji abụọ na topology nke isi site na iji Zorn's lemma, ha gosipụtara na ịdị adị nke Choquet-Bruhat n'elu na ịdị iche iche theorems na-akpaghị aka na-egosi na ụwa dị iche iche theorem:

 

Ihe akaebe Choquet-Bruhat na-eji nhọrọ dị nkọ nke nhazi, nhazi nke ebili mmiri (nke bụ Lorentzian nke kwekọrọ na nhazi nkwekọrịta), nke usoro nhazi nke Einstein na-aghọ usoro nke usoro ọdịiche dị iche iche nke hyperbolic, nke enwere ike itinye nsonaazụ dị mma.

== Ndụ onwe onye na ọnwụ ==
[[Faịlụ:Yvonne_Choquet-Bruhat_2.jpeg|thumb|Choquet-Bruhat n'afọ 2006]]
N'afọ 1947, ọ lụrụ onye mgbakọ na mwepụ ibe ya bụ Léonce Fourès. Nwa ha nwanyị bụ Michelle bụ onye na-ahụ maka gburugburu ebe obibi. Ọrụ ọkankuzi ya na nnyocha mbụ ya dị n'okpuru aha Yvonne Fourès-Bruhat. N'afọ 1960, Bruhat na Fourès gbara alụkwaghịm, o mechara lụọ onye mgbakọ na mwepụ Gustave Choquet ma gbanwee aha nna ya ka ọ bụrụ Choquet-Bruhat. Ya na Choquet nwere ụmụ abụọ; nwa ya nwoke, Daniel Choquet, bụ onye ọkà mmụta ụbụrụ ebe nwa ya nwanyị, Geneviève, bụ dọkịta.

Choquet-Bruhat nwụrụ na 11 Febụwarị 2025 na Merignac, France (33700), mgbe ọ dị afọ òtù narị na otu. 

== Akwụkwọ ndị bụ isi Ọ Bipụtara ==
**Isiokwu**

*  
* [Ihe e dere n'ala ala peeji] ''Akụkụ zuru ụwa ọnụ nke nsogbu Cauchy na General Relativity.'' [Ihe e dere n'ala ala peeji] mgbakọ na mwepụ. Phys. 14 (1969), 329–335.    

**Isiokwu nnyocha**

* Bruhat, Yvonne ''Nsogbu Cauchy.'' Gravitation: Nkwupụta maka nnyocha ugbu a, peeji nke 130-168, Wiley, New York, 1962.&nbsp;
* Choquet-Bruhat, Yvonne; York, James W. Jr. ''Nsogbu Cauchy.'' General Relativity and Gravity, Vol. 1, peeji nke 99-172, Plenum, New York-London, 1980.&nbsp;
* Choquet-Bruhat, Yvonne. ''Theorems nke ike dị mma.'' Relativity, òtù na topology, II (Les Houches, 1983), 739-785, North-Holland, Amsterdam, 1984.
* Choquet-Bruhat, Yvonne. ''Nsonaazụ na nsogbu ndị a emeghere na mgbakọ na mwepụ n'ozuzu.'' Milan J. Math 75 (2007), 273–289.
* Choquet-Bruhat, Yvonne. ''Mmalite nke nsogbu Cauchy maka usoro nhazi nke Einstein.'' Nnyocha na geometry dị iche iche 2015. Otu narị afọ nke General Relativity, 1-16, Surv. Ọ dị iche. Geom.

**Akwụkwọ teknụzụ**

* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile; Dillard-Bleick, Margaret. ''Analysis, manifolds and physics.'' Second edition. North-Holland Publishing Co., Amsterdam-New York, 1982. xx+630 pp.  
* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile. ''Analysis, manifolds and physics. Part II.'' North-Holland Publishing Co., Amsterdam, 1989. xii+449 pp.  
* Choquet-Bruhat, Y. ''Distributions.'' (French) Théorie et problèmes. Masson et Cie, Éditeurs, Paris, 1973. x+232 pp.
* Choquet-Bruhat, Yvonne. ''General relativity and the Einstein equations.'' Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009. xxvi+785 pp.  
* Choquet-Bruhat, Y. ''Géométrie différentielle et systèmes extérieurs.'' Préface de A. Lichnerowicz. Monographies Universitaires de Mathématiques, No. 28 Dunod, Paris 1968 xvii+328 pp.
* Choquet-Bruhat, Yvonne. ''Graded bundles and supermanifolds.'' Monographs and Textbooks in Physical Science. Lecture Notes, 12. Bibliopolis, Naples, 1989. xii+94 pp.  
* Choquet-Bruhat, Yvonne. ''Introduction to general relativity, black holes, and cosmology.'' With a foreword by Thibault Damour. Oxford University Press, Oxford, 2015. xx+279 pp.  
* Choquet-Bruhat, Y. ''Problems and solutions in mathematical physics.'' Translated from the French by C. Peltzer. Translation editor, J.J. Brandstatter Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam 1967 x+315 pp.

**Akwụkwọ ya a ma ama**

* Choquet-Bruhat, Yvonne. ''Nwaanyị na-eme mgbakọ na mwepụ na mbara igwe a dị ịtụnanya: ihe ncheta.'' A sụgharịrị ya site na 2016 French World Scientific Publishing Co. Pte. [Ihe e dere n'ala ala peeji] x+351 peeji nke   

== Ihe nrite ==

* Ihe nrite ọlaọcha nke National Center of Scientific Research, 1958
* Ihe nrite Henri de Parville nke Académie des Sciences, 1963
* Onye otu (site na 1965), Kọmitii Mba Nile nke Relativite Generale na Gravitation (onye isi oche 1980-1983) 
* Onye otu, Académie des Sciences, Paris (ahọpụtara 1979) 
* A họpụtara ya na American Academy of Arts and Sciences n'afọ 1985
* Njikọ maka ụmụ nwanyị na mgbakọ na mwepụ Noether Lecturer, 1986
* Onye Ọchịagha nke Legion of Honor, 1997
* Ihe nrite Dannie Heineman maka Mathematical Physics, 2003
* E buliri ya n'ọkwa ịbụ 'Grand Officier' na 'Grand Croix' na Légion d'Honneur n'afọ 2008. 

== Ebemsidee ==


== Njikọ mpụga ==


* [https://web.archive.org/web/20081202022121/http://www.physics.ucla.edu/~cwp/Phase2/Choquet-Bruhat,_Yvonne@922345678.html Enyemaka nke ụmụ nwanyị narị afọ nke iri abụọ na physics]
* [http://www.agnesscott.edu/lriddle/women/bruhat.htm "Yvonne Choquet-Bruhat", Akụkọ ndụ nke ụmụ nwanyị na-eme mgbakọ na mwepụ], Agnes Scott CollegeKọleji Agnes Scott
* 
* Nsụgharị Bekee nke akwụkwọ nke afọ 1952, Existence theorem maka usoro ụfọdụ nke nhazi ọdịiche na-abụghị nke ahịrị[https://www.mpiwg-berlin.mpg.de/sites/default/files/Preprints/P480.pdf Theorem nke ịdị adị maka usoro ụfọdụ nke nhazi ọdịiche na-abụghị nke ahịrị]


== Ọrụ ya ==
Site n'afọ 1949 ruo 1951 Bruhat bụụrụ onye enyemaka nnyocha na French National Centre for Scientific Research, n'ihi ya ọ natara nzere ọkankuzi ya.

N'afọ 1951, ọ ghọrọ onye nnyocha nwetarala nzere ọkankuzi na Institute for Advanced Study na Princeton, New Jersey. Onye nlekọta ọrụ ya, Jean Leray, tụrụ aro ka ọ mụọ usoro Nhazi nke Einstein (Einstein field Equations). O mekwara ọ mata [[Albert Einstein]], onye ọ gakwuuru ugboro ole na ole n'oge ọ nọ n'ụlọ akwụkwọ ahụ.

N'afọ 1952, e nyere Bruhat na di ya ọrụ na Marseilles, na-eme ka ọ pụọ n'oge na-adịghị anya n'ụlọ akwụkwọ ahụ. N'otu afọ ahụ, o bipụtara ịdị adị na ịbụ ihe pụrụ iche nke ụ́sà maka Usoro nhazi nke Einstein, bụ ọrụ ya kachasị ewu ewu. Ọrụ ya na-egosi ezi echiche nke usoro Einstein,  wee malite ọmụmụ nke dynamics in General Relativity.

N'afọ 1958, e nyere ya Ihe nrite ọlaọcha nke CNRS .  Site n'afọ 1958 ruo 1959 ọ kụziri ihe na Mahadum Reims . N'afọ 1960, ọ ghọrọ prọfesọ na ''Mahadum Pierre-et-Marie-Curie'' (UPMC) dị na Paris, ma nọgide na-abụ prọfesọ ma ọ bụ prọfesọ lara ezumike nká ruo mgbe ọ lara ezumike nká n'afọ 1992.
[[Faịlụ:Yvonne_Choquet-Bruhat,_Gustave_Choquet.jpeg|thumb|235x235px|Choquet-Bruhat na Gustave Choquet na Mahadum California, Berkeley, n'afọ 1974.]]
Na Mahadum Pierre et Marie Curie, ọ gara n'ihu na-eme ihe ntinye dị ukwuu na physics mgbakọ na mwepụ, ọkachasị na General Relativity, Supergravity, nakwa non-Abelian gauge theory of the standard model. Ọrụ ya n'afọ 1981 yana Demetrios Christodoulou gosipụtara ịdị adị nke ụ́sà zuru ụwa ọnụ nke Yang-Mills, Higgs, na usoro nhazi nke spinor na 3 + 1 Dimensions. Tụkwasị na nke a, n'afọ 1984, o mere ma eleghị anya ọmụmụ ihe mbụ nke onye na-eme mgbakọ na mwepụ mere nke supergravity nwere nsonaazụ nke enwere ike ịgbatị gaa na ihe nlereanya dị mkpa ugbu a na D=11 Dimensions.

N'afọ 1978, a họpụtara Yvonne Choquet-Bruhat ka ọ bụrụ onye nnọchi anya Academy of Sciences ma na 14 Mee 1979 ọ ghọrọ nwanyị mbụ a họpụtara ka ọ bụrụ onye òtù zuru oke. Site n'afọ 1980 ruo 1983 ọ bụụrụ onye isi oche nke **' ("Komiti mba ụwa na General Relativity na Gravitation"). N'afọ 1985, a họpụtara ya gaa na American Academy of Arts and Sciences. N'afọ 1986, a họpụtara ya ka ọ kụzie nkuzi a ma ama Noether Lecture nke Association for Women in Mathematics.

### Ihe Ntinye ya na Nnyocha teknụzụ
Nnyocha a ma ama nke Choquet-Bruhat na-ekwu maka ọdịdị mgbakọ na mwepụ nke usoro data mbụ nke General Relativity. Enwere ike ịkọwa nchịkọta nke nsonaazụ naanị n'ihe gbasara ihe dị iche iche dị iche iche.

* Ntọala M" style="font-style:italic;" typeof="M:Transclusion">g":{"wt":"mvar","href":"./Template:Mvar"},"params":{"1":{"wt":"M"}},"i":0}}]}' data-ve-no-generated-contents="true" id="mweg" style="font-style:italic;" typeof="mw:Transclusion">M">data mbụ bụ triplet k)"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mweQ" typeof="mw:Transclusion"> seetị data (*M*, *g*, *k*) nke M bụ ọnụọgụ atọ dị nro, g bụ ọnụọụọgụ Riemannian dị nro na M, na k bụ mpaghara dị nro (0,2) -tensor na M.
* Nyere data mbụ f":"./Template:Math"},"params":{"1":{"wt":"(M, g, k)"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mwgQ" typeof="mw:Transclusion">(*M*, *g*, *k*), **mmepe** nke (M,g, k) bụ Ụdị Lorentzian anọ (M, g) tinyere ntinye dị nro f: M → M na mpaghara vector dị nro n'akụkụ f nke mere na f *g = g na nke mere na ụdị nke abụọ nke f, n'ihe gbasara mpaghara vector e nyere, bụ k.

N'echiche a, enwere ike ile usoro data mbụ anya dị ka ntụziaka nke submanifold geometry nke embedded spacelike hypersurface dị  na Lorentzian manifold.

* Ntọala data mbụ (M, g, k) na-emezu usoro mgbochi ikuku, ma ọ bụ a na-ekwu na ọ bụ usoro data mbụ nke ikuku, ma ọ bụrụ na a na-emenụ mmusoro abụọ na-esonụ:

:: \begin{align}
R_g-|k|_g^2+(\operatorname{tr}_gk)^2&=0\\
\operatorname{div}_gk-d(\operatorname{tr}_gk)&=0.
\end{align}
: N'ebe a, g":{"wt":"math","href":"./Template:Math"},"params":{"1":{"wt":"Rg"}},"i":0}}]}" data-ve-no-generated-contents="true" id="mwmQ" typeof="mw:Transclusion">*R<sub>g</sub>* na-egosi nkwonkwo scalar nke g.

Otu n'ime nsonaazụ Choquet-Bruhat nke afọ 1952 na-ekwu ihe ndị a:

 

N'ikwu ya n'ụzọ dị nkenke, enwere ike ịchịkọta nke a dị ka ịsị na enwere oghere (M, g) nke f (M) bụ elu Cauchy. A na-akpọ mmepe dị otú ahụ mmepe ikuku zuru ụwa ọnụ. Choquet-Bruhat gosikwara na ọ bụ ihe pụrụ iche:

 

N'ụdị na-edoghị anya, nke a na-ekwu: nyere ihe ọ bụla dị ka oghere M nke Ricci-flat Lorentzian M M, geoM nke M dị nso na M bụ nke submanifold geometry nke m kpebiri n'ụzọ zuru ezu.

N'otu edemede ya na Robert Geroch dere n'afọ 1969, Choquet-Bruhat mere ka ọdịdị nke ịdị iche doo anya. Site na arụmụka peeji abụọ na topology nke isi site na iji Zorn's lemma, ha gosipụtara na ịdị adị nke Choquet-Bruhat n'elu na ịdị iche iche theorems na-akpaghị aka na-egosi na ụwa dị iche iche theorem:

 

Ọ bụ ihe a na-ahụkarị ugbua ịmụ maka ihe ndị dị otú ahụ. Dịka ọmụmaatụ, iwu a ma ama nke Demetrios Christodoulou na nke Sergiu Klainerman na nkwụsi ike nke oghere Minkowski na-ekwusi ike na ọ bụrụ na (R3, g, k) bụ data mbido nke nwere g na k nke dị nso na efu (n'ụdị ụfọdụ dị kpọmkwem), mgbe ahụ, mmepe ikuku hyperbolic ya zuru ụwa ọnụ bụ nke zuru ezu geodesically ma dịrịkwa nso geometrically na oghere Minkwski.

Ihe akaebe Choquet-Bruhat na-eji nhọrọ dị nkọ nke nhazi, nhazi nke ebili mmiri (nke bụ Lorentzian nke kwekọrọ na nhazi nkwekọrịta), nke usoro nhazi nke Einstein na-aghọ usoro nke usoro ọdịiche dị iche iche nke hyperbolic, nke enwere ike itinye nsonaazụ dị mma.

## Ndụ onwe onye na ọnwụ
thumb|Choquet-Bruhat n'afọ 2006
N'afọ 1947, ọ lụrụ onye mgbakọ na mwepụ ibe ya bụ Léonce Fourès. Nwa ha nwanyị bụ Michelle bụ onye na-ahụ maka gburugburu ebe obibi. Ọrụ ọkankuzi ya na nnyocha mbụ ya dị n'okpuru aha Yvonne Fourès-Bruhat. N'afọ 1960, Bruhat na Fourès gbara alụkwaghịm, o mechara lụọ onye mgbakọ na mwepụ Gustave Choquet ma gbanwee aha nna ya ka ọ bụrụ Choquet-Bruhat. Ya na Choquet nwere ụmụ abụọ; nwa ya nwoke, Daniel Choquet, bụ onye ọkà mmụta ụbụrụ ebe nwa ya nwanyị, Geneviève, bụ dọkịta.

Choquet-Bruhat nwụrụ na 11 Febụwarị 2025 na Merignac, France (33700), mgbe ọ dị afọ òtù narị na otu. 

## Akwụkwọ ndị bụ isi Ọ Bipụtara
**Isiokwu**

*  
* [Ihe e dere n'ala ala peeji] *Akụkụ zuru ụwa ọnụ nke nsogbu Cauchy na General Relativity.* [Ihe e dere n'ala ala peeji] mgbakọ na mwepụ. Phys. 14 (1969), 329–335.    

**Isiokwu nyocha**

* Bruhat, Yvonne *Nsogbu Cauchy.* Gravitation: Nkwupụta maka nyocha ugbu a, peeji nke 130-168, Wiley, New York, 1962.&nbsp;
* Choquet-Bruhat, Yvonne; York, James W. Jr. *Nsogbu Cauchy.* General Relativity and Gravity, Vol. 1, peeji nke 99-172, Plenum, New York-London, 1980.&nbsp;
* Choquet-Bruhat, Yvonne. *Theorems nke ike dị mma.* Relativity, otu na topology, II (Les Houches, 1983), 739-785, North-Holland, Amsterdam, 1984.
* Choquet-Bruhat, Yvonne. *Nsonaazụ na nsogbu ndị a na-emeghe na mgbakọ na mwepụ n'ozuzu.* [Ihe e dere n'ala ala peeji] 75 (2007), 273–289.
* Choquet-Bruhat, Yvonne. *Mmalite nke nsogbu Cauchy maka usoro nhazi nke Einstein.* Nnyocha na geometry dị iche iche 2015. Otu narị afọ nke General Relativity, 1-16, Surv. Ọ dị iche. Geom. [Ihe e dere n'ala ala peeji] [Ihe e dere n'ala ala peeji]

**Akwụkwọ teknụzụ**

* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile; Dillard-Bleick, Margaret. *Analysis, manifolds and physics.* Second edition. North-Holland Publishing Co., Amsterdam-New York, 1982. xx+630 pp.  
* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile. *Analysis, manifolds and physics. Part II.* North-Holland Publishing Co., Amsterdam, 1989. xii+449 pp.  
* Choquet-Bruhat, Y. *Distributions.* (French) Théorie et problèmes. Masson et Cie, Éditeurs, Paris, 1973. x+232 pp.
* Choquet-Bruhat, Yvonne. *General relativity and the Einstein equations.* Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009. xxvi+785 pp.  
* Choquet-Bruhat, Y. *Géométrie différentielle et systèmes extérieurs.* Préface de A. Lichnerowicz. Monographies Universitaires de Mathématiques, No. 28 Dunod, Paris 1968 xvii+328 pp.
* Choquet-Bruhat, Yvonne. *Graded bundles and supermanifolds.* Monographs and Textbooks in Physical Science. Lecture Notes, 12. Bibliopolis, Naples, 1989. xii+94 pp.  
* Choquet-Bruhat, Yvonne. *Introduction to general relativity, black holes, and cosmology.* With a foreword by Thibault Damour. Oxford University Press, Oxford, 2015. xx+279 pp.  
* Choquet-Bruhat, Y. *Problems and solutions in mathematical physics.* Translated from the French by C. Peltzer. Translation editor, J.J. Brandstatter Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam 1967 x+315 pp.

**Akwụkwọ ya a ma ama**

* Choquet-Bruhat, Yvonne. *Nwaanyị na-eme mgbakọ na mwepụ na mbara igwe a dị ịtụnanya: ihe ncheta.* A sụgharịrị ya site na 2016 French mbụ. World Scientific Publishing Co. Pte. [Ihe e dere n'ala ala peeji] x+351 peeji nke   

## Major publications
**Isiokwu**

*  
* [Ihe e dere n'ala ala peeji] *Akụkụ zuru ụwa ọnụ nke nsogbu Cauchy na General Relativity.* [Ihe e dere n'ala ala peeji] mgbakọ na mwepụ. Phys. 14 (1969), 329–335.    

**Isiokwu nnyocha**

* Bruhat, Yvonne *Nsogbu Cauchy.* Gravitation: Nkwupụta maka nnyocha ugbu a, peeji nke 130-168, Wiley, New York, 1962.&nbsp;
* Choquet-Bruhat, Yvonne; York, James W. Jr. *Nsogbu Cauchy.* General Relativity and Gravity, Vol. 1, peeji nke 99-172, Plenum, New York-London, 1980.&nbsp;
* Choquet-Bruhat, Yvonne. *Theorems nke ike dị mma.* Relativity, òtù na topology, II (Les Houches, 1983), 739-785, North-Holland, Amsterdam, 1984.
* Choquet-Bruhat, Yvonne. *Nsonaazụ na nsogbu ndị a emeghere na mgbakọ na mwepụ n'ozuzu.* Milan J. Math 75 (2007), 273–289.
* Choquet-Bruhat, Yvonne. *Mmalite nke nsogbu Cauchy maka usoro nhazi nke Einstein.* Nnyocha na geometry dị iche iche 2015. Otu narị afọ nke General Relativity, 1-16, Surv. Ọ dị iche. Geom.

**Akwụkwọ teknụzụ**

* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile; Dillard-Bleick, Margaret. *Analysis, manifolds and physics.* Second edition. North-Holland Publishing Co., Amsterdam-New York, 1982. xx+630 pp.  
* Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile. *Analysis, manifolds and physics. Part II.* North-Holland Publishing Co., Amsterdam, 1989. xii+449 pp.  
* Choquet-Bruhat, Y. *Distributions.* (French) Théorie et problèmes. Masson et Cie, Éditeurs, Paris, 1973. x+232 pp.
* Choquet-Bruhat, Yvonne. *General relativity and the Einstein equations.* Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009. xxvi+785 pp.  
* Choquet-Bruhat, Y. *Géométrie différentielle et systèmes extérieurs.* Préface de A. Lichnerowicz. Monographies Universitaires de Mathématiques, No. 28 Dunod, Paris 1968 xvii+328 pp.
* Choquet-Bruhat, Yvonne. *Graded bundles and supermanifolds.* Monographs and Textbooks in Physical Science. Lecture Notes, 12. Bibliopolis, Naples, 1989. xii+94 pp.  
* Choquet-Bruhat, Yvonne. *Introduction to general relativity, black holes, and cosmology.* With a foreword by Thibault Damour. Oxford University Press, Oxford, 2015. xx+279 pp.  
* Choquet-Bruhat, Y. *Problems and solutions in mathematical physics.* Translated from the French by C. Peltzer. Translation editor, J.J. Brandstatter Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam 1967 x+315 pp.

**Akwụkwọ ya a ma ama**

* Choquet-Bruhat, Yvonne. *Nwaanyị na-eme mgbakọ na mwepụ na mbara igwe a dị ịtụnanya: ihe ncheta.* A sụgharịrị ya site na 2016 French mbụ. World Scientific Publishing Co. Pte. [Ihe e dere n'ala ala peeji] x+351 peeji nke   
## Ihe nrite

* Ihe nrite ọlaọcha nke National Center of Scientific Research, 1958
* Ihe nrite Henri de Parville nke Académie des Sciences, 1963
* Onye otu (site na 1965), Kọmitii Mba Nile nke Relativite Generale na Gravitation (onye isi oche 1980-1983) 
* Onye otu, Académie des Sciences, Paris (ahọpụtara 1979) 
* A họpụtara ya na American Academy of Arts and Sciences n'afọ 1985
* Njikọ maka ụmụ nwanyị na mgbakọ na mwepụ Noether Lecturer, 1986
* Onye Ọchịagha nke Legion of Honor, 1997
* Ihe nrite Dannie Heineman maka Mathematical Physics, 2003
* E buliri ya n'ọkwa ịbụ 'Grand Officier' na 'Grand Croix' na Légion d'Honneur n'afọ 2008.

## Ebemsidee

## Njikọ mpụga

* Enyemaka nke ụmụ nwanyị narị afọ nke iri abụọ na physics
* "Yvonne Choquet-Bruhat", Akụkọ ndụ nke ụmụ nwanyị na-eme mgbakọ na mwepụ, Agnes Scott CollegeKọleji Agnes Scott
* 
* Nsụgharị Bekee nke akwụkwọ nke afọ 1952, Existence theorem maka usoro ụfọdụ nke nhazi ọdịiche na-abụghị nke ahịrịTheorem nke ịdị adị maka usoro ụfọdụ nke nhazi ọdịiche na-abụghị nke ahịrị

Otú:Ezinụlọ Bruhat
Otú:Ụmụ nwanyị
Otú:Ndị nwụrụ n'afọ 2025
Otú:Pages with unreviewed translations