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On open flat sets in spaces with bipolar comparison. / Lebedeva, Nina.

In: Geometriae Dedicata, Vol. 203, No. 1, 01.12.2019, p. 347-351.

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

Harvard

Lebedeva, N 2019, 'On open flat sets in spaces with bipolar comparison', Geometriae Dedicata, vol. 203, no. 1, pp. 347-351. https://doi.org/10.1007/s10711-019-00439-z

APA

Lebedeva, N. (2019). On open flat sets in spaces with bipolar comparison. Geometriae Dedicata, 203(1), 347-351. https://doi.org/10.1007/s10711-019-00439-z

Vancouver

Lebedeva N. On open flat sets in spaces with bipolar comparison. Geometriae Dedicata. 2019 Dec 1;203(1):347-351. https://doi.org/10.1007/s10711-019-00439-z

Author

Lebedeva, Nina. / On open flat sets in spaces with bipolar comparison. In: Geometriae Dedicata. 2019 ; Vol. 203, No. 1. pp. 347-351.

BibTeX

@article{2c8285c09d43470196bf8452dbd6b413,
title = "On open flat sets in spaces with bipolar comparison",
abstract = "We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.",
keywords = "Comparison geometry, Differential geometry, Metric geometry, Optimal transport, Rigidity",
author = "Nina Lebedeva",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s10711-019-00439-z",
language = "English",
volume = "203",
pages = "347--351",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - On open flat sets in spaces with bipolar comparison

AU - Lebedeva, Nina

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.

AB - We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.

KW - Comparison geometry

KW - Differential geometry

KW - Metric geometry

KW - Optimal transport

KW - Rigidity

UR - http://www.scopus.com/inward/record.url?scp=85063234302&partnerID=8YFLogxK

U2 - 10.1007/s10711-019-00439-z

DO - 10.1007/s10711-019-00439-z

M3 - Article

AN - SCOPUS:85063234302

VL - 203

SP - 347

EP - 351

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

ER -

ID: 126316067