From the 1 of 7 linked papers with an AI index.
7 papers
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 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,…
Computing renormalized curvature integrals on Poincaré-Einstein manifolds
Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin +2
We describe a general procedure for computing renormalized curvature integrals on Poincaré-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-ty…
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…
Holography and Cheeger constant of asymptotically CMC submanifolds
Samuel Pérez-Ayala, Aaron J. Tyrrell
Let be an asymptotically hyperbolic manifold. We compute the Cheeger constant of conformally compact asymptotically constant mean curvature submanifolds $ ι: Y^{k+…