6 papers
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…
Non-homothetic complete periodic contact forms with constant Tanaka--Webster scalar curvature
Jeffrey S. Case, Yuya Takeuchi
We study the existence problem for complete contact forms with constant Tanaka--Webster scalar curvature on non-compact strictly pseudoconvex CR manifolds. We prove that, under mil…
A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants
João Henrique Andrade, Jeffrey S. Case, Paolo Piccione +1
Given a conformally variational scalar Riemannian invariant , we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many no…
Nonhomothetic complete periodic metrics with constant scalar curvature
João H. Andrade, Jeffrey S. Case, Paolo Piccione +1
We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on $S^n\setminus S^k…
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…