Add to ORKG[[abstract]]Let H-l(p)(M) be the space of polynomial growth harmonic forms. We proved that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with a nonnegative curvature operator. In particular, this implies that the space of harmonic forms of fixed growth order on the Euclidean space with any periodic metric must be finite dimensional.[[fileno]]2010217010003[[department]]數學
In a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, ...
This thesis consists of six parts. In the first part, we give a general introduction of our topics. ...
The purpose of this note is to showcase a certain line of research that connects harmonic analysis, ...
In this paper, we give a sharp estimate on the dimension of the space of polynomial growth harmonic ...
[[abstract]]It is important and interesting to study harmonic functions on a Riemannian manifold. In...
[[abstract]]Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside...
Let Omega subset of R-n, n >= 3, and let p, 1 < p < infinity, p not equal D 2, be given. In...
We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient condition...
Consider an open Riemann surface R of Heins type, i.e., a parabolic Riemann surface with a single id...
Let A1,...,Ar be linear partial differential operators in N variables, with constant coefficients in a ...
In 1975, Yau proved that a complete manifold with nonnegative Ricci curvature must satisfy the Liovi...
We study n dimensional Riemanniann manifolds with harmonic forms of constant length and first Betti ...
For a noncompact harmonic manifold M we establish finite dimensionality of the eigensubspaces V-lamb...
ABSTRACT. We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient...
In this thesis we are concerned with estimating the regularity of ${\cal A}$-harmonic differential f...
In a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, ...
This thesis consists of six parts. In the first part, we give a general introduction of our topics. ...
The purpose of this note is to showcase a certain line of research that connects harmonic analysis, ...
In this paper, we give a sharp estimate on the dimension of the space of polynomial growth harmonic ...
[[abstract]]It is important and interesting to study harmonic functions on a Riemannian manifold. In...
[[abstract]]Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside...
Let Omega subset of R-n, n >= 3, and let p, 1 < p < infinity, p not equal D 2, be given. In...
We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient condition...
Consider an open Riemann surface R of Heins type, i.e., a parabolic Riemann surface with a single id...
Let A1,...,Ar be linear partial differential operators in N variables, with constant coefficients in a ...
In 1975, Yau proved that a complete manifold with nonnegative Ricci curvature must satisfy the Liovi...
We study n dimensional Riemanniann manifolds with harmonic forms of constant length and first Betti ...
For a noncompact harmonic manifold M we establish finite dimensionality of the eigensubspaces V-lamb...
ABSTRACT. We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient...
In this thesis we are concerned with estimating the regularity of ${\cal A}$-harmonic differential f...
In a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, ...
This thesis consists of six parts. In the first part, we give a general introduction of our topics. ...
The purpose of this note is to showcase a certain line of research that connects harmonic analysis, ...