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SUMMARY:Chao Xia/夏超 (Xiamen Uinversity)
DTSTART:20201227T091500Z
DTEND:20201227T100000Z
DTSTAMP:20260423T041344Z
UID:iccm2020/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/22/
 ">A sharp lower bound for the first (nonzero) Steklov eigenvalue</a>\nby C
 hao Xia/夏超 (Xiamen Uinversity) as part of ICCM 2020\n\n\nAbstract\nEsc
 obar has conjectured that for a compact manifold with boundary which has n
 onnegative Ricci curvature and boundary principal curvatures bounded below
  by 1\, the first (nonzero) Steklov eigenvalue is greater than or equal to
  1，with equality holding only on a Euclidean ball. This conjecture is tr
 ue in two dimensions due to Payne and Escobar. In this talk\, we present a
  resolution to this conjecture in the case of nonnegative sectional curvat
 ure in any dimensions. We will also give a sharp comparison result between
  the first (nonzero) Steklov eigenvalue and the boundary first eigenvalue.
  Our tool is a weighted Reilly type formula due to Qiu-Xia and a Pohozaev 
 type identity. The talk is based on a joint work with Changwei Xiong.\n
LOCATION:https://researchseminars.org/talk/iccm2020/22/
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