Delaunay-type hypersurfaces in cohomogeneity one manifolds

Abstract

Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction specializes to the classical examples in round spheres, and allows to obtain Delaunay-type hypersurfaces in many other ambient spaces, ranging from complex and quaternionic projective spaces to Kervaire exotic spheres.

LaTeX2e, 28 pages, final version

References in corpus (7)

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Cited by in corpus (6)

• Deformations of free boundary CMC hypersurfaces
• Equivariant bifurcation in geometric variational problems
• Full Laplace spectrum of distance spheres in symmetric spaces of rank one
• Parameterized splitting theorems and bifurcations for potential operators
• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
• Constant mean curvature surfaces of Delaunay type along a closed geodesic