Advances in Differential Equations

Uniqueness of constant weakly anisotropic mean curvature immersion of sphere $S^2$ in $\mathbb R^3$

Yoshikazu Giga and Jian Zhai

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Abstract

We prove that the constant anisotropic mean curvature immersion of the sphere $S^2$ in $ \mathbb R^3$ is unique, provided that anisotropy is weak in the sense that the energy density function is close to the isotropic one.

Article information

Source
Adv. Differential Equations Volume 14, Number 7/8 (2009), 601-619.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867227

Mathematical Reviews number (MathSciNet)
MR2527686

Zentralblatt MATH identifier
1183.53053

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53B40: Finsler spaces and generalizations (areal metrics) 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Giga, Yoshikazu; Zhai, Jian. Uniqueness of constant weakly anisotropic mean curvature immersion of sphere $S^2$ in $\mathbb R^3$. Adv. Differential Equations 14 (2009), no. 7/8, 601--619. https://projecteuclid.org/euclid.ade/1355867227.


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