Doubling Property for Bilipschitz Homogeneous Geodesic Surfaces

نویسنده

  • ENRICO LE DONNE
چکیده

In this paper we discuss general properties of geodesic surfaces that are (locally) biLipschitz homogeneous. In particular, we prove that they are locally doubling and there exists a special doubling measure analogous to the Haar measure for locally compact groups.

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

Geodesic Manifolds with a Transitive Subset of Smooth Bilipschitz Maps

This paper is connected with the problem of describing path metric spaces which are homeomorphic to manifolds and biLipschitz homogeneous, i.e., whose biLipschitz homeomorphism group acts transitively. Our main result is the following. LetX = G/H be a homogeneous space of a Lie group G, and let d be a geodesic distance on X inducing the same topology. Suppose there exists a subgroup GS of G whi...

متن کامل

ec 2 01 3 INVERSE LIMIT SPACES SATISFYING A POINCARÉ INEQUALITY

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...

متن کامل

Numerical Treatment of Geodesic Differential Equations on Two Dimensional Surfaces

This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.

متن کامل

Volume of spheres in doubling metric measured spaces and in groups of polynomial growth

Let G be a compactly generated locally compact group and let U be a compact generating set. We prove that if G has polynomial growth, then (U)n∈N is a Følner sequence and we give a polynomial estimate of the rate of decay of μ(Un+1 r Un) μ(Un) . Our proof uses only two ingredients: the doubling property and a weak geodesic property that we call Property (M). As a matter of fact, the result rema...

متن کامل

2 01 3 Inverse Limit Spaces Satisfying a Poincaré Inequality

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...

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 2008