Rigidity for metrics with the same lengths of Geodesics

Plamen Stefanov; Gunther Uhlmann

doi:10.4310/MRL.1998.v5.n1.a7

Rigidity for metrics with the same lengths of Geodesics

Plamen Stefanov^*, Gunther Uhlmann

^*Corresponding author for this work

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

69 Citations (Scopus)

Abstract

We prove that we can recover a Riemannian metric in a bounded smooth domain in ℝ³ up to an isometry which is the identity on the boundary, by knowing the lengths of the geodesics joining points on the boundary. We assume that the metrics are close to the euclidian metric e.

Original language	English
Pages (from-to)	83-96
Number of pages	14
Journal	Mathematical Research Letters
Volume	5
Issue number	1-2
DOIs	https://doi.org/10.4310/MRL.1998.v5.n1.a7
Publication status	Published - 1998
Externally published	Yes

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10.4310/MRL.1998.v5.n1.a7

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title = "Rigidity for metrics with the same lengths of Geodesics",

abstract = "We prove that we can recover a Riemannian metric in a bounded smooth domain in ℝ3 up to an isometry which is the identity on the boundary, by knowing the lengths of the geodesics joining points on the boundary. We assume that the metrics are close to the euclidian metric e.",

author = "Plamen Stefanov and Gunther Uhlmann",

year = "1998",

doi = "10.4310/MRL.1998.v5.n1.a7",

language = "English",

volume = "5",

pages = "83--96",

journal = "Mathematical Research Letters",

issn = "1073-2780",

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TY - JOUR

T1 - Rigidity for metrics with the same lengths of Geodesics

AU - Stefanov, Plamen

AU - Uhlmann, Gunther

PY - 1998

Y1 - 1998

N2 - We prove that we can recover a Riemannian metric in a bounded smooth domain in ℝ3 up to an isometry which is the identity on the boundary, by knowing the lengths of the geodesics joining points on the boundary. We assume that the metrics are close to the euclidian metric e.

AB - We prove that we can recover a Riemannian metric in a bounded smooth domain in ℝ3 up to an isometry which is the identity on the boundary, by knowing the lengths of the geodesics joining points on the boundary. We assume that the metrics are close to the euclidian metric e.

UR - https://openalex.org/W2127436860

UR - https://www.scopus.com/pages/publications/0032219315

U2 - 10.4310/MRL.1998.v5.n1.a7

DO - 10.4310/MRL.1998.v5.n1.a7

M3 - Journal Article

SN - 1073-2780

VL - 5

SP - 83

EP - 96

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 1-2

ER -

Rigidity for metrics with the same lengths of Geodesics

Abstract

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