Relations between Sobolev and Kantorovich norms on manifolds with curvature conditions

نویسندگان

  • V. I. Bogachev
  • A. V. Shaposhnikov
  • F.-Yu. Wang
چکیده

We prove several multiplicative inequalities relating the Kantorovich norm with the Sobolev norm for functions on a Riemannian manifold satisfying certain curvature conditions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

متن کامل

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

متن کامل

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

متن کامل

Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds

We give a new proof of a theorem of Bourgain [4], asserting that solutions of linear Schrödinger equations on the torus, with smooth time dependent potential, have Sobolev norms growing at most like t when t→ +∞, for any > 0. Our proof extends to Schrödinger equations on other examples of compact riemannian manifolds.

متن کامل

the International Congress of Chinese Mathematicians Fine Analysis of

Blow up analysis has been very useful in the study of nonlinear partial diier-ential equations. Usually blow up analysis is done with respect to energy norms, namely, giving asymptotic description in Sobolev norms to a sequence of solutions (or approximate solutions) of nonlinear partial diierential equations. In a number of applications, pointwise asymptotic analysis is needed. This is a ner b...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016