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Renormalized Area of Catenoids in the Hyperbolic Space
Alvaro Pampano, Aaron J. Tyrrell
We show that the generating curves of non-totally geodesic spherical rotational minimal hypersurfaces (catenoids, for simplicity) of the hyperbolic spaces are $…
Renormalized area of minimal surfaces in hyperbolic space
Matthew J. Gursky, Khoi Nguyen, Aaron J. Tyrrell
In this paper we consider minimal surfaces in hyperbolic space of arbitrary codimension that are critical for renormalized area. We give two criteria which imply that must be a…
Topological and rigidity results for four-dimensional hypersurfaces in space forms
Davide Dameno, Aaron J. Tyrrell
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First,…
Local and global conformal invariants of submanifolds
Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin +2
We develop methods for constructing and computing conformal invariants of submanifolds, with a particular emphasis on conformal submanifold scalars and conformally invariant integr…