Open Access
October, 2017 Stability and bifurcation for surfaces with constant mean curvature
Miyuki KOISO, Bennett PALMER, Paolo PICCIONE
J. Math. Soc. Japan 69(4): 1519-1554 (October, 2017). DOI: 10.2969/jmsj/06941519


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 ${\mathbb R}^3$.


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Miyuki KOISO. Bennett PALMER. Paolo PICCIONE. "Stability and bifurcation for surfaces with constant mean curvature." J. Math. Soc. Japan 69 (4) 1519 - 1554, October, 2017.


Published: October, 2017
First available in Project Euclid: 25 October 2017

zbMATH: 1382.58012
MathSciNet: MR3715814
Digital Object Identifier: 10.2969/jmsj/06941519

Primary: 58E12
Secondary: 49Q10 , 49R05 , 53A10

Keywords: bifurcation , Constant mean curvature surfaces , stability

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 4 • October, 2017
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