Some Remarks on Uniformly Regular Riemannian Manifolds

Abstract

We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.

References in corpus (3)

• Anisotropic Function Spaces on Singular Manifolds
• Continuous maximal regularity on uniformly regular Riemannian manifolds
• A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows

Cited by in corpus (12)

• Analysis on singular spaces: Lie manifolds and operator algebras
• Singular parabolic equations of second order on manifolds with singularities
• Quantitative null-cobordism
• The Yamabe flow on incomplete manifolds
• Continuous maximal regularity on singular manifolds and its applications
• Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and Hölder Spaces on Uniformly Regular Riemannian Manifolds
• Maximal Regularity of Parabolic Transmission Problems
• On the flow of non-axisymmetric perturbations of cylinders via surface diffusion
• The wave equation with acoustic boundary conditions on non-locally reacting surfaces
• Heat Kernels, Solvable Lie Groups, and the Mean Reverting SABR Stochastic Volatility Model
• Function Spaces on Uniformly Regular and Singular Riemannian Manifolds
• Analysis and boundary value problems on singular domains: an approach via bounded geometry