A capillary interpolation framework produces new minimal surfaces in spheres as non-trivial sphere bundles over base spaces including Stiefel manifolds, projective planes over division algebras, and Lie group quotients, with uniqueness for rotationally symmetric cases.
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Characterizations of stable and weakly stable minimal capillary surfaces with near-extreme capillary angles are given on minimal or positive-mean-curvature supports, using curvature estimates to analyze tangential limits.
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Topology of minimal surfaces in the sphere from capillarity
A capillary interpolation framework produces new minimal surfaces in spheres as non-trivial sphere bundles over base spaces including Stiefel manifolds, projective planes over division algebras, and Lie group quotients, with uniqueness for rotationally symmetric cases.
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Tangential limits of stable minimal capillary surfaces
Characterizations of stable and weakly stable minimal capillary surfaces with near-extreme capillary angles are given on minimal or positive-mean-curvature supports, using curvature estimates to analyze tangential limits.