Peter TOPPING - Sharp local decay estimates for the Ricci flow on surfaces
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2016-06-03

There  are  many  tools  available  when  studying  2D  Ricci  flow,  equivalently  the logarithmic fast diffusion equation, but one has always been missing: how do you get uniform smoothing estimates in terms of local L^1 data, i.e. in terms of local bounds 
on the area. The problem is that the direct analogue of the geometrically less-useful L^p  smoothing  estimates  for  p bigger than 1  are  simply  false.  In  this  talk  I  will  explain  this problem  in  more  detail,  and  show  how  to  get  around  it  with  a  new  local  decay 
estimate.  I  also  plan  to  sketch  the  proof  and/or  give  some  applications.  No knowledge   of   Ricci   flow   will   be   assumed