The Kannan's fixed point theorem in a cone rectangular metric space.
Stability results for rotationally invariant constant mean curvature surfaces in hyperbolic space
We prove the existence of many constant mean curvature surfaces of revolution with two ends which are immersed or embedded in hyperbolic space. We also study their stability.
Construction of compact constant mean curvature hypersurfaces with topology
In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.
End-to-end gluing of constant mean curvature hypersurfaces
It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.
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