Donnerstag, 06.06.2024: Sharp pinching theorems for submanifolds in the sphere
Fernanda Roing (University of Turin)
We prove that every complete, minimally immersed submanifold (Formel) whose
second fundamental form satisfies (Formel) , is either totally geodesic, or (a covering of)
a Clifford torus or a Veronese surface in , thereby extending the well- known results by
Simons, Lawson and Chern, do Carmo & Kobayashi from compact to complete (Formel). We
also obtain the corresponding result for complete hypersurfaces with nonvanishing
constant mean curvature, due to Alencar & do Carmo in the compact case, under the
optimal bound on the umbilicity tensor. Our approach is inspired by the conformal method
of Fischer-Colbrie, Shen & Ye and Catino, Mastrolia & Roncoroni. This is a joint work with
M. Magliaro, M. Mari and A. Savas-Halilaj.
| Uhrzeit: |
14:00 |
| Ort: |
Seminarraum S09 (C6H05) and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: |
Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: |
Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
