Isoperimetric structure of asymptotically conical manifolds
نویسندگان
چکیده
منابع مشابه
Deformations of Asymptotically Conical Special Lagrangian Submanifolds
The naive approach is to parametrize these deformations as the zero-set of a “mean curvature operator”, then study them using the implicit function theorem. However, this entails a good understanding of the Jacobi operator of the initial submanifold Σ, which in general is not possible. The work of Oh and, more recently, of McLean (cfr. [Oh], [ML]) shows that, in the “right” geometric context, t...
متن کاملRigidity of Asymptotically Hyperbolic Manifolds
In this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity and a volume comparison theorem.
متن کاملDynamics of Asymptotically Hyperbolic Manifolds
We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. This result generalizes the classical theorem of Duistermaat-Guillemin for compact manifolds and the results of GuillopéZworski, Perry, and Guillarmou-Naud...
متن کاملIsoperimetric-type inequalities on constant curvature manifolds
By exploiting optimal transport theory on Riemannian manifolds and adapting Gromov’s proof of the isoperimetric inequality in the Euclidean space, we prove an isoperimetric-type inequality on simply connected constant curvature manifolds.
متن کاملIsoperimetric Conditions and Diffusions in Riemannian Manifolds
We study diiusions in Riemannian manifolds and properties of their exit time moments from smoothly bounded domains with compact closure. For any smoothly bounded domain with compact closure, ; and for each positive integer k; we characterize the kth exit time moment of Brownian motion, averaged over the domain with respect to the metric density, using a variational quotient. We prove that for R...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2017
ISSN: 0022-040X
DOI: 10.4310/jdg/1483655857