Harmonic Functions of Polynomial Growth on Singular spaces with nonnegative Ricci Curvature
نویسندگان
چکیده
In the present paper, the Liouville theorem and the finite dimension theorem of polynomial growth harmonic functions are proved on Alexandrov spaces with nonnegative Ricci curvature in the sense of Sturm, Lott-Villani and Kuwae-Shioya.
منابع مشابه
On Function Theory on Spaces with a Lower Ricci Curvature Bound
In this announcement, we describe some results of an ongoing investigation of function theory on spaces with a lower Ricci curvature bound. In particular, we announce results on harmonic functions of polynomial growth on open manifolds with nonnegative Ricci curvature and Euclidean volume growth.
متن کاملRicci Curvature and Convergence of Lipschitz Functions
We give a definition of convergence of differential of Lipschitz functions with respect to measured Gromov-Hausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic cones of manifolds with nonnegative Ricci curvature and Euclidean volume growth, and distributional Laplacian comparison theorem on limit spaces of Riemannian ma...
متن کاملHarmonic Functions of Linear Growth on Kähler Manifolds with Nonnegative Ricci Curvature
The subject began in 1975, when Yau [Y1] proved that there are no nonconstant, positive harmonic functions on a complete manifold with nonnegative Ricci curvature. A few years later, Cheng [C] pointed out that using a local version of Yau’s gradient estimate, developed in his joint work with Yau [CY], one can show that there are no nonconstant harmonic functions of sublinear growth on a manifol...
متن کاملHarmonic Functions with Polynomial Growth Deenition 0.2. for an Open (complete Noncompact) Manifold, M N , given a Point P 2 M Let R Be the Distance from P. Deene H D (m) to Be
Twenty years ago Yau, 56], generalized the classical Liouville theorem of complex analysis to open manifolds with nonnegative Ricci curvature. Speciically, he proved that a positive harmonic function on such a manifold must be constant. This theorem of Yau was considerably generalized by Cheng-Yau (see 15]) by means of a gradient estimate which implies the Harnack inequality. As a consequence o...
متن کاملul 2 00 4 Harmonic homogeneous manifolds of nonpositive curvature
A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010