Harmonic Functions with given Values and Minimum Norms in Riemannian Spaces.

نویسندگان

  • L Sario
  • N Fukuda
چکیده

We use the standard notations: differential forms ap, their exterior algebra A, exterior derivative d<p, Hodge's star operator *, coderivative 3f = (_ 1)nP + n 1*d*(P, Laplace-Beltrami operator A = d3 + Md, exterior product (pAg,, inner product (so,*) = fJmpA*4p, and the Dirichlet norm D(sp) = (dep, dp) + (a<p, 5op). For 0forms u the norm reduces to D(u) = (du, du), and Au has the representation

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

Harmonic Maps into Trees and Graphs - Analytical and Numerical Aspects

The main topic of this work is the definition and investigation of a nonlinear energy for maps with values in trees and graphs and the analysis of the corresponding nonlinear Dirichlet problem. The nonlinear energy is defined using a semigroup approach based on Markov kernels and the nonlinear Dirichlet problem is given as a minimizing problem of the nonlinear energy. Conditions for the existen...

متن کامل

Weak Fubini Property and Infinity Harmonic Functions in Riemannian and Sub-riemannian Manifolds

We examine the relationship between infinity harmonic functions, absolutely minimizing Lipschitz extensions, strong absolutely minimizing Lipschitz extensions, and absolutely gradient minimizing extensions in CarnotCarathéodory spaces. Using the weak Fubini property we show that absolutely minimizing Lipschitz extensions are infinity harmonic in any sub-Riemannian manifold.

متن کامل

Some Classifications of ∞-harmonic Maps between Riemannian Manifolds

∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞harmonic maps from and into a sphere, quadratic ∞-harmonic maps between Euclidean spaces. We describe all linear and quadratic ∞-harmonic maps between Nil and Euclidean spaces, be...

متن کامل

Curvature Conditions on Riemannian Manifolds with Brownian Harmonicity Properties

The time and place that Brownian motion on a Riemannian manifold first exits a normal ball of radius e is considered and a general procedure is given for computing asymptotic expansions, as e decreases to zero, for joint moments of the first exit time and place random variables. It is proven that asymptotic versions of exit time and place distribution properties that hold on harmonic spaces are...

متن کامل

N ov 2 00 4 Notes on Stein - Sahi representations and some problems of non L 2 harmonic analysis Neretin

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces. Recently, Oshima [67] published his formula for c-function for L 2 on pseudo-Riemannian symmetric spaces (see also works of Delorm [12] and van den Ban– Schlichtkrull [3], [4]). After this, there arises a natural question about other solvable problems of non-commutative harmonic analysis. In the Appendix to the paper...

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:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 53 2  شماره 

صفحات  -

تاریخ انتشار 1965