Almost invariant submanifolds for compact group actions
Alan Weinstein
Abstract
We define a C1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney's idea of realizing submanifolds as zeros of sections of extended normal bundles.
Create a lesson
Related papers
Topological and spectral rigidity of hypersurface Zoll manifolds
Gustavo Martins
Stationary varifolds with singularities II
Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al.
Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities
Mitchell Gaudet
Deformations of harmonic maps with conical singularities
Dominik Gutwein, Thibault Langlais
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song