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pro vyhledávání: '"Gursky, Matthew J."'
We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of the boundary
Externí odkaz:
http://arxiv.org/abs/2407.08851
Autor:
Gover, A. Rod, Gursky, Matthew J.
Let $(M^4,g)$ be a smooth, closed, oriented anti-self-dual (ASD) four-manifold. $(M^4,g)$ is said to be unobstructed if the cokernel of the linearization of the self-dual Weyl tensor is trivial. This condition can also be characterized as the vanishi
Externí odkaz:
http://arxiv.org/abs/2307.12432
Autor:
Gursky, Matthew J.
Publikováno v:
In Journal of Geometry and Physics August 2024 202
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 prove a Gauss-Bonnet theorem for the renormalized volume, and compute its
Externí odkaz:
http://arxiv.org/abs/2101.11755
Publikováno v:
Journal of Functional Analysis Volume 282, Issue 8, 15 April 2022, 109371
Let $(M^n,g)$ be a closed Riemannian manifold of dimension $n\ge 3$. Assume $[g]$ is a conformal class for which the Conformal Laplacian $L_g$ has at least two negative eigenvalues. We show the existence of a (generalized) metric that maximizes the s
Externí odkaz:
http://arxiv.org/abs/2010.13210
Autor:
Gursky, Matthew J., Zhang, Siyi
In the article we consider Bach-flat metrics on four-manifolds with boundary, with conformally invariant boundary conditions. We show that such metrics arise naturally as critical points of the Weyl energy under a constraint. We then prove a rigidity
Externí odkaz:
http://arxiv.org/abs/2007.04355
Autor:
Graham, C. Robin, Gursky, Matthew J.
We derive a formula of Chern-Gauss-Bonnet type for the Euler characteristic of a four dimensional manifold-with-boundary in terms of the geometry of the Loewner-Nirenberg singular Yamabe metric in a prescribed conformal class. The formula involves th
Externí odkaz:
http://arxiv.org/abs/1902.01562
We prove a conformally invariant estimate for the index of Schr\"odinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the inde
Externí odkaz:
http://arxiv.org/abs/1901.04539
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