The boundary distance function and the Dirichlet-to-Neumann map

Leonid Pestov; Gunther Uhlmann

doi:10.4310/mrl.2004.v11.n3.a2

The boundary distance function and the Dirichlet-to-Neumann map

Leonid Pestov^*, Gunther Uhlmann

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

3 Citations (Scopus)

Abstract

We outline the proof that two dimensional simple Riemannian manifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.

Original language	English
Pages (from-to)	285-297
Number of pages	13
Journal	Mathematical Research Letters
Volume	11
Issue number	2-3
DOIs	https://doi.org/10.4310/mrl.2004.v11.n3.a2
Publication status	Published - 2004
Externally published	Yes

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10.4310/mrl.2004.v11.n3.a2

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title = "The boundary distance function and the Dirichlet-to-Neumann map",

abstract = "We outline the proof that two dimensional simple Riemannian manifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.",

author = "Leonid Pestov and Gunther Uhlmann",

year = "2004",

doi = "10.4310/mrl.2004.v11.n3.a2",

language = "English",

volume = "11",

pages = "285--297",

journal = "Mathematical Research Letters",

issn = "1073-2780",

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T1 - The boundary distance function and the Dirichlet-to-Neumann map

AU - Pestov, Leonid

AU - Uhlmann, Gunther

PY - 2004

Y1 - 2004

N2 - We outline the proof that two dimensional simple Riemannian manifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.

AB - We outline the proof that two dimensional simple Riemannian manifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000222671600012

UR - https://openalex.org/W2087770593

UR - https://www.scopus.com/pages/publications/3543004721

U2 - 10.4310/mrl.2004.v11.n3.a2

DO - 10.4310/mrl.2004.v11.n3.a2

M3 - Journal Article

SN - 1073-2780

VL - 11

SP - 285

EP - 297

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2-3

ER -

The boundary distance function and the Dirichlet-to-Neumann map

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