Analysis Seminar: Asaf Shachar (HUJI) — Non-Euclidean elasticity: Embedding manifolds with minimal distortion

Location: Ross 70A and Zoom
https://huji.zoom.us/j/88693310302?pwd=cjZDOWhhMmJSaFVrdHhMZ0JlOVRHUT09

Title: Non-Euclidean elasticity: Embedding manifolds with minimal distortion

Abstract: Given two dimensional Riemannian manifolds $M,N$, I will present a sharp lower bound on the elastic energy (distortion) of embeddings $f:M \to N$, in terms of the areas' discrepancy of $M,N$.
The minimizing maps attaining this bound go through a phase transition when the ratio of areas is $1/4$: The homotheties are the unique energy minimizers when the ratio $\frac{V_N}{V_M} \ge 1/4$, and they cease being minimizers when $\frac{V_N}{V_M}$ gets below $1/4$.
I will describe explicit minimizers in the non-trivial regime $\frac{V_N}{V_M} < 1/4$ when $M,N$ are disks, and give a proof sketch of the lower bound. If time permits, I will discuss the stability of minimizers.

Date: 

Wed, 21/04/2021 - 12:00 to 13:00