Gaussian mean curvature flow for submanifolds in space forms

Aleksander Borisenko; Vladimir Rovenski

doi:10.1007/978-3-319-04675-4__2

Gaussian mean curvature flow for submanifolds in space forms

Aleksander Borisenko
, Vladimir Rovenski

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this chapter we investigate the convergence of the mean curvature flow of submanifolds in Euclidean and hyperbolic spaces with Gaussian density. For Euclidean case, we prove that the flow deforms a closed submanifold with pinching condition to a “round point” in finite time.

Original language	English
Title of host publication	Geometry and its Applications
Editors	Pawel Walczak, Vladimir Rovenski
Publisher	Springer New York LLC
Pages	39-50
Number of pages	12
ISBN (Electronic)	9783319046747
DOIs	https://doi.org/10.1007/978-3-319-04675-4__2
State	Published - 2014
Event	2nd International workshop Geometry and Symbolic Computation, 2013 - Haifa, Israel Duration: 15 May 2013 → 18 May 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	72
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	2nd International workshop Geometry and Symbolic Computation, 2013
Country/Territory	Israel
City	Haifa
Period	15/05/13 → 18/05/13

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2014.

Keywords

Conformal transformation
Density
Mean curvature flow
Riemannian metric

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-04675-4__2

Cite this

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title = "Gaussian mean curvature flow for submanifolds in space forms",

abstract = "In this chapter we investigate the convergence of the mean curvature flow of submanifolds in Euclidean and hyperbolic spaces with Gaussian density. For Euclidean case, we prove that the flow deforms a closed submanifold with pinching condition to a “round point” in finite time.",

keywords = "Conformal transformation, Density, Mean curvature flow, Riemannian metric",

author = "Aleksander Borisenko and Vladimir Rovenski",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.; 2nd International workshop Geometry and Symbolic Computation, 2013 ; Conference date: 15-05-2013 Through 18-05-2013",

year = "2014",

doi = "10.1007/978-3-319-04675-4\_\_2",

language = "English",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "39--50",

editor = "Pawel Walczak and Vladimir Rovenski",

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Borisenko, A & Rovenski, V 2014, Gaussian mean curvature flow for submanifolds in space forms. in P Walczak & V Rovenski (eds), Geometry and its Applications. Springer Proceedings in Mathematics and Statistics, vol. 72, Springer New York LLC, pp. 39-50, 2nd International workshop Geometry and Symbolic Computation, 2013, Haifa, Israel, 15/05/13. https://doi.org/10.1007/978-3-319-04675-4__2

Gaussian mean curvature flow for submanifolds in space forms. / Borisenko, Aleksander; Rovenski, Vladimir.
Geometry and its Applications. ed. / Pawel Walczak; Vladimir Rovenski. Springer New York LLC, 2014. p. 39-50 (Springer Proceedings in Mathematics and Statistics; Vol. 72).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Rovenski, Vladimir

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2014.

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N2 - In this chapter we investigate the convergence of the mean curvature flow of submanifolds in Euclidean and hyperbolic spaces with Gaussian density. For Euclidean case, we prove that the flow deforms a closed submanifold with pinching condition to a “round point” in finite time.

AB - In this chapter we investigate the convergence of the mean curvature flow of submanifolds in Euclidean and hyperbolic spaces with Gaussian density. For Euclidean case, we prove that the flow deforms a closed submanifold with pinching condition to a “round point” in finite time.

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KW - Density

KW - Mean curvature flow

KW - Riemannian metric

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ER -

Gaussian mean curvature flow for submanifolds in space forms

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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