A. Shachar

activity

20162021

most citedOn the role of curvature in the elastic energy of non-Euclidean thin bodies

16 citations · 28 across the 4 of their papers we have counts for

collaborators

6 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★ 1 cited

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…

math.AP2018★ 16 cited

On the role of curvature in the elastic energy of non-Euclidean thin bodies

Cy Maor, Asaf Shachar

We prove a relation between the scaling $h^{β}$ of the elastic energies of shrinking non-Euclidean bodies $S_{h}$ of thickness $h \to 0$ , and the curvature along their mid-surface $S$ .…

math.DG2017★ 9 cited

Reshetnyak rigidity for Riemannian manifolds

Raz Kupferman, Cy Maor, Asaf Shachar

We prove two rigidity theorems for maps between Riemannian manifolds. First, we prove that a Lipschitz map $f : M \to N$ between two oriented Riemannian manifolds, whose differential…

math.DG2016★ 2 cited

On strain measures and the geodesic distance to $SO_{n}$ in the general linear group