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Renormalized Area of Catenoids in the Hyperbolic Space
Alvaro Pampano, Aaron J. Tyrrell
The paper analyzes rotational minimal hypersurfaces (catenoids) in odd‑dimensional hyperbolic space, showing their generating curves are p‑elastic and deriving an explicit formula…
Renormalized Area of Hypersurfaces in Hyperbolic Spaces
Alvaro Pampano
We employ Chen's conformal invariant quantity [8, Theorem 1] in combination with the Chern-Gauss-Bonnet formulas to obtain expressions for the renormalized area of asymptotically m…
Hyperbolic Geometry and the Helfrich Functional
Bennett Palmer, Alvaro Pampano
The Helfrich model is a fundamental tool for determining the morphology of biological membranes. We relate the geometry of an important class of its equilibria to the geometry of s…
Closed -Elastic Curves in Spheres of
Alvaro Pampano, Miraj Samarakkody, Hung Tran
For every , we study -elastic curves in the hyperbolic plane and in the de Sitter -space . We analyze the existence of closed $…