1 citations · 1 across the 12 of their papers we have counts for
13 papers
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…
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+1…
Self-dual and even Poincaré-Einstein metrics in dimension four
Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré…
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-typ…
First Eigenvalue Estimates for Asymptotically Hyperbolic Manifolds and their Submanifolds
Samuel Pérez-Ayala, Aaron J. Tyrrell
We derive a sharp upper bound for the first eigenvalue of the -Laplacian on asymptotically hyperbolic manifolds for . We then prove that a particular class…
A Gauss-Bonnet formula for the renormalized area of minimal submanifolds of Poincaré-Einstein manifolds
Jeffrey S. Case, C Robin Graham, Tzu-Mo Kuo +2
Assuming the extrinsic -curvature admits a decomposition into the Pfaffian, a scalar conformal submanifold invariant, and a tangential divergence, we prove that the renormalized…
A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces
Jeffrey S. Case, Aaron J. Tyrrell
We derive a sharp inequality relating the second and fourth elementary symmetric functions of the eigenvalues of a trace-free matrix and give two applications. First, we give a new…
A Rigidity Result for Minimal Rotation Hypersurfaces of 5D Spaces of Constant Curvature
Aaron J. Tyrrell
In this paper we show that a particular extrinsic pointwise hypersurface invariant is always non-positive on minimal hypersurfaces of constant curvature spaces and vanishes identic…
Renormalized Area for Minimal Hypersurfaces of 5D Poincaré-Einstein Spaces
Aaron J. Tyrrell
In this paper we derive a Gauss-Bonnet formula for the renormalized area of Graham-Witten minimal hypersurfaces of 5-dimensional Poincaré-Einstein spaces. The formula we derive exp…
Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces
Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
We define a renormalized volume for a region in an asymptotically hyperbolic Einstein manifold that is bounded by a Graham-Witten minimal surface and the conformal infinity. We pro…