Mean curvature flow of graphs in warped products
Authors:
Alexander A. Borisenko and Vicente Miquel
Journal:
Trans. Amer. Math. Soc. 364 (2012), 45514587
MSC (2010):
Primary 53C44; Secondary 53C40, 53C21
Published electronically:
April 11, 2012
MathSciNet review:
2922601
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Additional Information
Abstract: Let be a complete Riemannian manifold which is either compact or has a pole, and let be a positive smooth function on . In the warped product , we study the flow by the mean curvature of a locally Lipschitz continuous graph on and prove that the flow exists for all time and that the evolving hypersurface is for and is a graph for all . Moreover, under certain conditions, the flow has a welldefined limit.
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Additional Information
Alexander A. Borisenko
Affiliation:
Mathematics Faculty, Geometry Department, Kharkov National University, Pl. Svobodi 4, 61077Kharkov, Ukraine
Email:
borisenk@univer.kharkov.ua
Vicente Miquel
Affiliation:
Departamento de Geometría y Topología, Universidad de Valencia, Avda. Andrés Estellés 1, 46100Burjassot (Valencia) Spain
Email:
miquel@uv.es
DOI:
http://dx.doi.org/10.1090/S000299472012054250
Keywords:
Differential geometry,
algebraic geometry
Received by editor(s):
January 30, 2009
Received by editor(s) in revised form:
July 12, 2010
Published electronically:
April 11, 2012
Additional Notes:
This work was done while the first author was Visiting Professor at the University of Valencia in 2008, supported by a \lq\lq ayuda del Ministerio de Educación y Ciencia SAB20060073.” He wants to thank that university and its Department of Geometry and Topology for the facilities they gave him.
The second author was partially supported by the DGI(Spain) and FEDER Project MTM20101544 and the Generalitat Valenciana Project Prometeo 2009/099
Both authors want to thank the referee for pointing out a mistake in a previous version of the paper.
Dedicated:
Dedicated to Professor Antonio M. Naveira on the occasion of his 70th birthday
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
