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- W3040931057 abstract "Let [Formula: see text] be a three-dimensional Lie group with a bi-invariant metric. Consider [Formula: see text] a strictly convex domain in [Formula: see text]. We prove that if [Formula: see text] is a stable CMC free-boundary surface in [Formula: see text] then [Formula: see text] has genus either 0 or 1, and at most three boundary components. This result was proved by Nunes [I. Nunes, On stable constant mean curvature surfaces with free-boundary, Math. Z. 287(1–2) (2017) 73–479] for the case where [Formula: see text] and by R. Souam for the case where [Formula: see text] and [Formula: see text] is a geodesic ball with radius [Formula: see text], excluding the possibility of [Formula: see text] having three boundary components. Besides [Formula: see text] and [Formula: see text], our result also apply to the spaces [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. When [Formula: see text] and [Formula: see text] is a geodesic ball with radius [Formula: see text], we obtain that if [Formula: see text] is stable then [Formula: see text] is a totally umbilical disc. In order to prove those results, we use an extended stability inequality and a modified Hersch type balancing argument to get a better control on the genus and on the number of connected components of the boundary of the surfaces." @default.
- W3040931057 created "2020-07-16" @default.
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- W3040931057 date "2020-08-18" @default.
- W3040931057 modified "2023-10-16" @default.
- W3040931057 title "On stable CMC free-boundary surfaces in a strictly convex domain of a bi-invariant Lie group" @default.
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- W3040931057 doi "https://doi.org/10.1142/s0129167x2050086x" @default.
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