Liouville's rigidity theorem (1850) states that a map $f:\Omega\subset R^d \to R^d$ that satisfies $Df \in SO(d)$ is an affine map. Reshetnyak (1967) generalized this result and showed that if a sequence $f_n$ satisfies $Df_n \to SO(d)$ in $L^p$, then $f_n$ converges to an affine map. In this talk I will discuss generalizations of these theorems to mappings between manifolds and sketch the main ideas of the proof (using techniques from the calculus of variations and from harmonic analysis). Finally, I will describe how these rigidity questions are related to weak notions of convergence of manifolds and present some open questions. Based on a joint work with Asaf Shachar and Raz Kupferman.
Thu, 15/12/2016 - 14:30 to 15:30
Manchester Building (Hall 2), Hebrew University Jerusalem