A. Shachar

collaborators

3 papers

math.AP2021

Embedding surfaces inside small domains with minimal distortion

Asaf Shachar

Given two-dimensional Riemannian manifolds $M, N$ , we prove a lower bound on the distortion of embeddings $M \to N$ , in terms of the areas' d…

math.DG2018

A geometric perspective on the Piola identity in Riemannian settings

Raz Kupferman, Asaf Shachar

The Piola identity $div cof \nabla f = 0$ is a central result in the mathematical theory of elasticity. We prove a generalized version of the Piola iden…

math.DG2018

Regularity via minors and applications to conformal maps

Asaf Shachar

We prove that if the minors of degree $k$ of a Sobolev map $R^{d} \to R^{d}$ are smooth then the map is smooth, when $k, d$ are not both even. We use this result to de…