Journal of the Mathematical Society of Japan

Stability and bifurcation for surfaces with constant mean curvature

Miyuki KOISO, Bennett PALMER, and Paolo PICCIONE

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Abstract

We give criteria for the existence of smooth bifurcation branches of fixed boundary CMC surfaces in $\mathbb R^3$, and we discuss stability/instability issues for the surfaces in bifurcating branches. To illustrate the theory, we discuss an explicit example obtained from a bifurcating branch of fixed boundary unduloids in ${\mathbb R}^3$.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 4 (2017), 1519-1554.

Dates
First available in Project Euclid: 25 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1508918567

Digital Object Identifier
doi:10.2969/jmsj/06941519

Mathematical Reviews number (MathSciNet)
MR3715814

Zentralblatt MATH identifier
1382.58012

Subjects
Primary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90] 49R05: Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)

Keywords
bifurcation constant mean curvature surfaces stability

Citation

KOISO, Miyuki; PALMER, Bennett; PICCIONE, Paolo. Stability and bifurcation for surfaces with constant mean curvature. J. Math. Soc. Japan 69 (2017), no. 4, 1519--1554. doi:10.2969/jmsj/06941519. https://projecteuclid.org/euclid.jmsj/1508918567


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