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math.DG2024
Deformations of the scalar curvature of a partially integrable pseudohermitian manifold
Jeffrey S. Case, Pak Tung Ho
We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In par…
math.DG2024
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…
math.DG2024
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…