L^p-Sobolev inequalities on minimal submanifolds

2024/12/11 by Balogh, Zoltán M., Kristály, Alexandru, Mester, Ágnes
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.08408

Abstract

The paper is devoted to proving Allard-Michael-Simon-type L^p-Sobolev inequalities (p>1) with explicit constants in the setting of Euclidean minimal submanifolds of arbitrary codimension. Our results require separate discussions for the cases p≥ 2 and 1

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