Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-12T23:31:32.575Z Has data issue: false hasContentIssue false

Manifolds Without Green’s Formula*

Published online by Cambridge University Press:  22 January 2016

Moses Glasner*
Affiliation:
California Institute of TechnologyPasadena, California 91109
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently attention has been focused on manifolds that carry covariant tensors that are merely bounded measurable. In terms of these tensors global differential equations are defined and their weak solutions are called harmonic functions. Nakai initiated the classification of these manifolds with respect to the global properties of the harmonic functions that they carry.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

Footnotes

*

Supported in part by the National Science Foundation, Grant GP 14133.

References

[1] Glasner, M., The principal operators L0 and L1 the Royden boundary, J. Analyse Math. 24 (1971), 163172.CrossRefGoogle Scholar
[2] Glasner, M., Dirichlet mappings of Riemannian manifolds and the equation Δu — Pu, J. Differential Equations, 9 (1971), 390404.Google Scholar
[3] Katz, M. Glasner—R., The Royden boundary of a Riemannian manifold, Ill. J. Math., (1970).Google Scholar
[4] Hervé, R.M., Quelques propriétés des sursolutions et sursolutions locales d’une équation uniformément elliptique de la forme , Ann. Inst. Fourier, Grenoble 16 (1966), 241267.Google Scholar
[5] Maeda, F-Y., Introduction to a potential theory on a differentiable manifold, Lecture notes, Kyoto University, October 1968.Google Scholar
[6] Nakai, M., On parabolicity and Royden compactifications of Riemannian manifolds, Proc. International Congress Functional Analysis, 1969.Google Scholar
[7] Nakai, M., Royden algebra and quasi-isometries of Riemannian manifolds, Pacific J. Math, (to appear).Google Scholar
[8] Sario, B. Rodin—L., Principal functions, D. Van Nostrand Co., 1968.Google Scholar
[9] Nakai, L. Sario—M., Classification of Riemann surfaces, Springer-Verlag, 1970.Google Scholar
[10] Sario—M., L. Glasner, Schiffer—M., The span and principal functions in Riemannian spaces, J. Analyse Math. 15 (1965), 115134.Google Scholar
[11] Stampacchia, G., Le probleme de Dirichlet pour les èquations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Grenoble 15 (1965), 189258.Google Scholar
[12] Walsh, B., Flux in axiomatic potential theory, Inventiones Math. 8 (1969) 175221.Google Scholar