Semicontinuity of Isometry Groups and Isomorphism Groups: a Survey

Abstract

Isomorphisms that preserve a certain geometric structure are easily destroyed by an arbitrary small deformation of the structure, but restoring them requires a definite amount of change. Such an intuitive understanding has actually been established as precise theorems, via Lie groups, Riemannian geometry, and several complex variables. The aim of this paper is to present a concise but comprehensive exposition. © 2019, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.