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SUMMARY:Wei Yuan/袁伟 (Sun Yat-sen University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260423T024030Z
UID:iccm2020/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/14/
 ">Volume comparison with respect to scalar curvature</a>\nby Wei Yuan/袁
 伟 (Sun Yat-sen University) as part of ICCM 2020\n\n\nAbstract\nIn Rieman
 nian geometry\, volume comparison theorem is one of the most fundamental r
 esults. The classic results concern volume comparison involving restrictio
 ns on Ricci curvature. In this talk\, we will investigate the volume compa
 rison with respect to scalar curvature. In particular\, we show that one c
 an only expect such results for small geodesic balls of metrics near V-sta
 tic metrics. As for closed manifolds\, we give a volume comparison theorem
  for metrics near stable Einstein metrics. In particular\, it provides par
 tially affirmative answers to both a conjecture of Schoen about hyperbolic
  manifolds and a conjecture proposed by Bray concerning the positive scala
 r curvature case respectively.\n
LOCATION:https://researchseminars.org/talk/iccm2020/14/
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