Shiu-Yuen Cheng

Shiu-Yuen Cheng (鄭紹遠) ko ganndo hiisiwal to Hong Kong. O wonii hannde hooreejo porfeseer hiisa to duɗal jaaɓi haaɗtirde ganndal e karallaagal to Hong Kong. Cheng heɓi doktoraa mum Ph.D. e hitaande 1974, e gardagol Shiing-Shen Chern, ummoriiɗo to duɗal jaaɓi haaɗtirde Kaliforni to Berkeley.Ndeen Cheng waɗii duuɓi seeɗa e golle makko caggal doktoraa e balloowo jannginoowo to duɗal jaaɓi haaɗtirde Princeton e duɗal jaaɓi haaɗtirde dowla New York to Stony Brook. Ndeen o wonti porfeseer timmuɗo to duɗal jaaɓi haaɗtirde Kaliforni to Los Angeles. Cheng ardii departemaaji Hiisawal to Duɗal Jaaɓihaaɗtirde Siin to Hong Kong e Duɗal Jaaɓihaaɗtirde Ganndal e Karallaagal Hong Kong e kitaale 1990. E hitaande 2004, o wonti Deenoowo ganndal to HKUST. E hitaande 2012, o wonti tergal fedde hiisawal Amerik.

O anndaama no feewi e darnde makko e joometiri feere-feere e pottitte feere-feere feccere, ina jeyaa heen miijo nannditgol eigenvalue Cheng, miijo Cheng jowitiingo e njaajeendi ɓurndi mawnude, e golle keewɗe e Shing-Tung Yau . Golle Cheng e Yau keewɗe ina njeyaa e korpus golle ɗe Yau rokkaa njeenaari Fields e hitaande 1982. Gila hitaande 2020, golle wiɗto Cheng ɓurɗe ɓadaade ɗee njaltinaa ko e hitaande 1996.

## Darnde karallaagal

### Estimaaji gradient e kuutoragol mum en
E hitaande 1975, Shing-Tung Yau heɓi limngal kesal ngam saabaade pottitte ceertuɗe elliptik gonɗe e doggol ɗiɗaɓol e dow won e mbaydiiji Riemannian timmuɗi.  Cheng e Yau mbaawii ƴellitde limto Yau ngoo e huutoraade feere nde Eugenio Calabi ƴetti . [CY75] Njiylawu oo, anndiraango limto mbaylaandi Cheng–Yau, ina tawee e kala nokku e fannu ƴeewndo joometiri . Ko ɗum waɗi, Cheng e Yau mbaawii hollirde woodde gollal keeringal, nanndungal e teddeendi keeringal gadanal, golloowo Laplace-Beltrami e dow manifolde Riemannian timmunde.

Cheng e Yau kuutoriima ngool laawol ngam faamde hipersurfaaji nannduɗi e weeyo Minkowski e joometiri hipersurfaaji e nder weeyo affine . [CY76a] [CY86] Kuutoragol keeringol njeñtudi maɓɓe ko teskuyaaji Bernstein wonande hipersurfaaji nannduɗi e weeyo udditiiɗi e weeyo Minkowski mo njuuteendi mum woni no feewi ; kala hipersurface hono noon ina foti wonde dingiral. [CY76a]

Nder hitaande 1916, Hermann Weyl heɓti anndal feere-feere ngam dogginki joometiri dow ko laaɓi nder weeyo Euclidean. E huutoraade doosgal ɓurngal mawnude, o waawii jogaade doole joometiri yaajndi to bannge joometiri ndernderi. Cheng e Yau kuutoriima ɗum e ngonka hipersurfaaji e nder mbaydiiji Riemannian. [CY77b]

### Caɗeele Minkowski e pottital Monge-Ampère
Kala hipersurface udditirɗo no feewi e nder weeyo Euclidean ℝn + 1 ina waawi siforeede no mbaydi n -dimensionnel sfera, rewrude e kartal Gauss . Caɗeele Minkowski ina naamnoo so tawii gollal ɓuuɓngal e moƴƴal gonngal e dow tagofeere n -dimensionnel ina waawi feeñde no ɓuuɓol skalaar ngol metrik Riemann ngol ngalɗoo nanondiral addani. Ɗumɗoon noon, ko Louis Nirenberg, ƴetti ɗum e hitaande 1953, e nder haala ka n foti ko e ɗiɗi.  E hitaande 1976, Cheng e Yau ndartini caɗeele ɗee e kuuɓal. [CY76b]

E kuutoragol waylo-waylo Legendre, kuutorɗe pottital Monge-Ampère ina ndokka kadi hipersurfaaji ɓuuɓɗi e weeyo Euclide ; ɓuuɓol skalaar ngol metrik ndernderiijo ngol ko bannge ñaamo pottital Monge-Ampère ngal yamiri. Ko noon ne kadi, Cheng e Yau mbaawi huutoraade ƴeewndo mum en caɗeele Minkowski ngam heɓde humpitooji ko faati e ƴeewndo pottitte Monge-Ampère. [CY77a] Ko ɗum kuutorgal keeringal, ɓe keɓii miijo gonngo e keertinagol kuuɓtodinngo adanngo wonande caɗeele keeri-nafoore wonande pottital Monge-Ampère. Luis Caffarelli, Nirenberg e Joel Spruck caggal ɗuum ƴettii laabi ɓurɗi yooɗde ngam haɓaade ngool caɗeele. 

## Binndanɗe mawɗe
 

## Tuugnorgal