relative volume comparison theorems in finsler geometry and their applications

نویسندگان

bing ye wu

department of mathematics minjiang university

چکیده

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

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

Relative volume comparison theorems in Finsler geometry and their applications

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

متن کامل

5 Comparison Theorems in Finsler Geometry and Their Applications

We prove Hessian comparison theorems, Laplacian comparison theorems and volume comparison theorems of Finsler manifolds under various curvature conditions. As applications, we derive Mckean type theorems for the first eigenvalue of Finsler manifolds, as well as generalize a result on fundamental group due to Milnor to Finsler manifolds.

متن کامل

Some Generalized Comparison Results in Finsler Geometry and Their Applications

In this paper, we generalize the Hessian comparison theorems and Laplacian comparison theorems described in [16, 18], then give some applications under various curvature conditions.

متن کامل

Comparison Theorems in Pseudo-hermitian Geometry and Applications

In this paper, we study the theory of geodesics with respect to the TanakaWebster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some HopfRinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.

متن کامل

Comparison Theorems in Riemannian Geometry

The subject of these lecture notes is comparison theory in Riemannian geometry: What can be said about a complete Riemannian manifold when (mainly lower) bounds for the sectional or Ricci curvature are given? Starting from the comparison theory for the Riccati ODE which describes the evolution of the principal curvatures of equidistant hypersurfaces, we discuss the global estimates for volume a...

متن کامل

Unicorns in Finsler Geometry

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

متن کامل

منابع من

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


عنوان ژورنال:
bulletin of the iranian mathematical society

جلد ۴۰، شماره ۱، صفحات ۲۱۷-۲۳۴

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023