Stability of boundary distance representation and reconstruction of riemannian manifolds

Atsushi Katsuda, Yaroslav Kurylev, Matti Lassas

研究成果: Contribution to journalArticle査読

11 被引用数 (Scopus)

抄録

A boundary distance representation of a Riemannian manifold with boundary (M, g, ∂M) is the set of functions {rx ∈ C(∂M): x ∈ M}, where rx are the distance functions to the boundary, rx(z) = d(x, z), z ∈ ∂M. In this paper we study the question whether this representation determines the Riemannian manifold in a stable way if this manifold satisfies some a priori geometric bounds. The answer is affermative, moreover, given a discrete set of approximate boundary distance functions, we construct a finite metric space that approximates the manifold (M, g) in the Gromov-Hausdorff topology. In applications, the boundary distance representation appears in many inverse problems, where measurements are made on the boundary of the object under investigation. As an example, for the heat equation with an unknown heat conductivity the boundary measurements determine the boundary distance representation of the Riemannian metric which corresponds to this conductivity.

本文言語英語
ページ(範囲)135-157
ページ数23
ジャーナルInverse Problems and Imaging
1
1
DOI
出版ステータス出版済み - 2007
外部発表はい

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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