Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
Singular Isoperimetric Hypersurfaces and CMC Hypersurfaces under Perturbed Riemannian Metrics
Gongping Niu (The Chinese University of Hong Kong)
Abstract
It is known that isoperimetric hypersurfaces in a smooth, compact (n+1)-manifold are smooth except for a closed set of singularities with codimension at least 7. This is also an optimal estimate with singular examples constructed in [Niu24]. So in the specific case where n+1 = 8, there exist manifolds with singular isoperimetric hypersurfaces, prompting the question of whether all isoperimetric hypersurfaces are generically smooth. This talk will discuss the asymptotic rate of the induced Jacobi field near some isolated singular points and explore how it implies the removal of singularities for isoperimetric or constant mean curvature (CMC) hypersurfaces with perturbed Riemannian metrics.
Meeting ID: 813 4901 8845
Passcode: 567950
Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chung-Jun Tsai (NTU)
