Continuous maximal regularity on uniformly regular Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
Continuous maximal regularity on uniformly regular Riemannian manifolds
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on uniformly regular Riemannian manifolds M. As an application, we show that solutions to the Yamabe flow on M instantaneously regularize and become real analytic in space and time. The regularity result is obtained by introducing a family of parameter-dependent diffeomor...
متن کاملUniformly Elliptic Operators on Riemannian Manifolds
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev inequalities on geodesic balls. Then we u...
متن کاملRiemannian Manifolds with Uniformly Bounded Eigenfunctions
The standard eigenfunctions φλ = ei〈λ,x〉 on flat tori Rn/L have L-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L2normalized eigenfunctions have uniformly bounded L-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum co...
متن کاملMaximal Complexifications of Certain Homogeneous Riemannian Manifolds
Let M = G/K be a homogeneous Riemannian manifold with dimCGC = dimRG, where GC denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and natur...
متن کاملRiemannian Manifolds with Maximal Eigenfunction Growth
On any compact Riemannian manifold (M,g) of dimension n, the Lnormalized eigenfunctions {φλ} satisfy ||φλ||∞ ≤ Cλ n−1 2 where −∆φλ = λ 2φλ. The bound is sharp in the class of all (M, g) since it is obtained by zonal spherical harmonics on the standard n-sphere S. But of course, it is not sharp for many Riemannian manifolds, e.g. flat tori R/Γ. We say that S, but not R/Γ, is a Riemannian manifol...
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 Evolution Equations
سال: 2014
ISSN: 1424-3199,1424-3202
DOI: 10.1007/s00028-014-0218-6