Zobrazeno 1 - 10
of 196
pro vyhledávání: '"Case, Jeffrey"'
Autor:
Case, Jeffrey S.
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G8, Pp 1375-1382 (2023)
The Rumin algebra of a contact manifold is a contact invariant $C_\infty $-algebra of differential forms which computes the de Rham cohomology algebra. We recover this fact by giving a simple and explicit construction of the Rumin algebra via Markl
Externí odkaz:
https://doaj.org/article/f030fecf7c0940b49c2e7d564d32e762
Autor:
Case, Jeffrey S., Yan, Zetian
We prove that the curved Ovsienko--Redou operators and a related family of differential operators are formally self-adjoint. This verifies two conjectures of Case, Lin, and Yuan.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2405.09532
We describe a general procedure for computing renormalized curvature integrals on Poincar\'e-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-type formulas of Albin and Chang-Qing-Yang for the renormalized volume,
Externí odkaz:
http://arxiv.org/abs/2404.11319
Autor:
Case, Jeffrey S., Ho, Pak Tung
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 particular, we introduce and discuss $R$-singular spaces, give sufficient
Externí odkaz:
http://arxiv.org/abs/2404.07002
Assuming the extrinsic $Q$-curvature admits a decomposition into the Pfaffian, a scalar conformal submanifold invariant, and a tangential divergence, we prove that the renormalized area of an even-dimensional minimal submanifold of a Poincar\'e-Einst
Externí odkaz:
http://arxiv.org/abs/2403.16710
We show that the half-ball in $\mathbb{R}^4$ can be conformally changed so that the only contribution to the Gauss--Bonnet formula is a constant term at the corner. This may be seen as a fourth-order Cherrier--Escobar-type problem on the half-ball.
Externí odkaz:
http://arxiv.org/abs/2401.00937
Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a closed Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also identify a
Externí odkaz:
http://arxiv.org/abs/2310.15798
Autor:
Case, Jeffrey S., Malchiodi, Andrea
We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product $H^{\ell} \times S^{d-\ell}$. We also show that the
Externí odkaz:
http://arxiv.org/abs/2310.12013
Autor:
Case, Jeffrey S.
We simplify V\'etois' Obata-type argument and use it to identify a closed interval $I_n$, $n \geq 3$, containing zero such that if $a \in I_n$ and $(M^n,g)$ is a closed conformally Einstein manifold with nonnegative scalar curvature and $Q_4 + a\sigm
Externí odkaz:
http://arxiv.org/abs/2309.12431
We derive extrinsic GJMS operators and $Q$-curvatures associated to a submanifold of a conformal manifold. The operators are conformally covariant scalar differential operators on the submanifold with leading part a power of the Laplacian in the indu
Externí odkaz:
http://arxiv.org/abs/2306.11294