Problems of unique determination of domains by the relative metrics on\n their boundaries

2016/08/15 by A. P. Kopylov, Kopylov, Anatoly P.
Mathematics · #53C45 #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1608.04270

openalex publication_date 2016/08/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This survey is devoted to discussing the problems of the unique determination\nof surfaces that are the boundaries of (generally speaking) nonconvex domains.\n First (in Sec. 2) we examine some results on the problem of the unique\ndetermination of domains by the relative metrics of the boundaries. Then, in\nSec. 3, we study rigidity conditions for the boundaries of submanifolds in a\nRiemannian manifold. The final part (Sec. 4) is concerned with the unique\ndetermination of domains by the condition of the local isometry of boundaries\nin the relative metrics.\n The survey in particular contains the results of arXiv:1401.7295,\narXiv:1305.6169, arXiv:1511.04235.\n

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