The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds

DOI10.1090/S0002-9947-96-01496-1zbMath0867.53007MaRDI QIDQ4875777

Antonio Ros, Manuel Ritoré

Publication date: 11 August 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

nonexistencecompactnessconstant mean curvature surfaceshigher genus surfacesflat three-manifoldsindex one minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20)

Related Items (12)

Double Bubbles in the Three-Torus ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ Embedded minimal surfaces: Forces, topology and symmetries ⋮ The isoperimetric problem for lens spaces ⋮ Isoperimetry and volume preserving stability in real projective spaces ⋮ Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions ⋮ An isoperimetric comparison theorem for Schwarzschild space and other manifolds ⋮ Index one minimal surfaces in spherical space forms ⋮ A note on constant geodesic curvature curves on surfaces ⋮ On stability and index of minimal submanifolds ⋮ The periodic isoperimetric problem ⋮ Isoperimetric inequalities in crystallography

Cites Work

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• Stable complete minimal surfaces in 𝑅³ are planes
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V

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