Soliton solutions of the mean curvature flow and minimal hypersurfaces

Authors:
Norbert Hungerbühler and Thomas Mettler

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2117-2126

MSC (2010):
Primary 49Q05

DOI:
https://doi.org/10.1090/S0002-9939-2011-11205-X

Published electronically:
October 21, 2011

MathSciNet review:
2888198

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an oriented Riemannian manifold of dimension at least and a vector field. We show that the Monge-Ampère differential system (M.A.S.) for -pseudosoliton hypersurfaces on is equivalent to the minimal hypersurface M.A.S. on for some Riemannian metric if and only if is the gradient of a function , in which case . Counterexamples to this equivalence for surfaces are also given.

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Additional Information

**Norbert Hungerbühler**

Affiliation:
Department of Mathematics, ETH Zürich, CH-8092 Zurich, Switzerland

Email:
norbert.hungerbuehler@math.ethz.ch

**Thomas Mettler**

Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, California 94720

Email:
mettler@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-11205-X

Keywords:
Mean curvature flow,
soliton solutions,
minimal hypersurfaces,
Monge-Ampère systems,
equivalence problem

Received by editor(s):
February 11, 2011

Published electronically:
October 21, 2011

Additional Notes:
Research for this article was carried out while the authors were supported by the Swiss National Science Foundation, the first author by the grant 200020-124668, and the second by the postdoctoral fellowship PBFRP2-133545.

Communicated by:
Jianguo Cao

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.