Geometric Analysis and Mathematical Relativity Seminar ——Index and topology of minimal hypersurfaces in R^n
主 题: Geometric Analysis and Mathematical Relativity Seminar ——Index and topology of minimal hypersurfaces in R^n
报告人: Dr. Chao Li (Stanford University)
时 间: 2017-12-25 14:30-16:30
地 点: Room 1303, Science Building No. 1
We consider immersed two-sided minimal hypersurfaces in R^n with finite total curvature. We prove that the sum of the Morse index and the nullity of the Jacobi operator is bounded from below by a linear function of the number of ends and the first Betti number of the hypersurface. When n=4, we are able to drop the nullity term by a careful study for the rigidity case. Our result is the first effective generalization of Li-Wang. Using our index estimates and ideas from the recent work of Chodosh-Ketover-Maximo, we prove compactness and finiteness results of minimal hypersurfaces in R^4 with finite index.
