Geometry and stability of surfaces with constant anisotropic mean curvature

Miyuki Koiso; Bennett Palmer

doi:10.1512/iumj.2005.54.2613

Geometry and stability of surfaces with constant anisotropic mean curvature

Miyuki Koiso, Bennett Palmer

Research output: Contribution to journal › Review article › peer-review

40 Citations (Scopus)

Abstract

We study the geometry of surfaces which are in equilibrium for a (constant coefficient) parametric elliptic functional with a volume constraint. We consider the first and second variations and the exceptional set of the Gauss map for such surfaces. The equilibrium surfaces of revolution (anisotropic Delaunay surfaces) are also discussed as is an anisotropic version of the Willmore functional.

Original language	English
Pages (from-to)	1817-1852
Number of pages	36
Journal	Indiana University Mathematics Journal
Volume	54
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2005.54.2613
Publication status	Published - Jan 1 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1512/iumj.2005.54.2613

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abstract = "We study the geometry of surfaces which are in equilibrium for a (constant coefficient) parametric elliptic functional with a volume constraint. We consider the first and second variations and the exceptional set of the Gauss map for such surfaces. The equilibrium surfaces of revolution (anisotropic Delaunay surfaces) are also discussed as is an anisotropic version of the Willmore functional.",

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AU - Palmer, Bennett

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N2 - We study the geometry of surfaces which are in equilibrium for a (constant coefficient) parametric elliptic functional with a volume constraint. We consider the first and second variations and the exceptional set of the Gauss map for such surfaces. The equilibrium surfaces of revolution (anisotropic Delaunay surfaces) are also discussed as is an anisotropic version of the Willmore functional.

AB - We study the geometry of surfaces which are in equilibrium for a (constant coefficient) parametric elliptic functional with a volume constraint. We consider the first and second variations and the exceptional set of the Gauss map for such surfaces. The equilibrium surfaces of revolution (anisotropic Delaunay surfaces) are also discussed as is an anisotropic version of the Willmore functional.

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DO - 10.1512/iumj.2005.54.2613

M3 - Review article

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EP - 1852

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

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ER -

Geometry and stability of surfaces with constant anisotropic mean curvature

Abstract

All Science Journal Classification (ASJC) codes

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