Volume entropy based on integral Ricci curvature and volume ratio

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Volume Geodesic Distortion and Ricci Curvature for Hamiltonian Dynamics

We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics introduced in [4], appear in the exp...

متن کامل

Volume Geodesic Distorsion and Ricci Curvature for Hamiltonian Dynamics

We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics introduced in [4], appear in the exp...

متن کامل

Manifolds of Positive Ricci Curvature with Almost Maximal Volume

10. In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below. The well-known theorems of Myers and Bishop imply that a manifold M n with Ric ~ n 1 satisfies diam(1l1n) ~ diam(Sn(I)), Vol(Mn) ~ Vol(Sn(I)). It follows from [Ch] that equality in either of these estimates can be achieved only if M n is isometric to Sn (1). The natural conjecture is that a manif...

متن کامل

Ricci curvature, entropy and optimal transport

This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability measures characterizes lower bounds of the Ricci curvature. We then discuss geometric properties of general metric measure spaces satisfying this convexity condition. Mathematics Subject Classificatio...

متن کامل

On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct ...

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

ژورنال

عنوان ژورنال: Differential Geometry and its Applications

سال: 2008

ISSN: 0926-2245

DOI: 10.1016/j.difgeo.2007.11.009