On Stokes’ theorem for noncompact manifolds
HTML articles powered by AMS MathViewer
- by Leon Karp PDF
- Proc. Amer. Math. Soc. 82 (1981), 487-490 Request permission
Abstract:
Stokes’ theorem was first extended to noncompact manifolds by Gaffney. This paper presents a version of this theorem that includes Gaffney’s result (and neither covers nor is covered by Yau’s extension of Gaffney’s theorem). Some applications of the main result to the study of subharmonic functions on noncompact manifolds are also given.References
- Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130. MR 175148, DOI 10.1007/BF02684398
- Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR 0169148
- S. Bochner, Curvature and Betti numbers, Ann. of Math. (2) 49 (1948), 379–390. MR 25238, DOI 10.2307/1969287
- Matthew P. Gaffney, A special Stokes’s theorem for complete Riemannian manifolds, Ann. of Math. (2) 60 (1954), 140–145. MR 62490, DOI 10.2307/1969703
- R. E. Greene and H. Wu, Integrals of subharmonic functions on manifolds of nonnegative curvature, Invent. Math. 27 (1974), 265–298. MR 382723, DOI 10.1007/BF01425500
- Alfred Huber, On subharmonic functions and differential geometry in the large, Comment. Math. Helv. 32 (1957), 13–72. MR 94452, DOI 10.1007/BF02564570
- Leon Karp, Subharmonic functions on real and complex manifolds, Math. Z. 179 (1982), no. 4, 535–554. MR 652859, DOI 10.1007/BF01215065 S. Kobayashi and K. Nomizu, Foundations of differential geometry. I, Interscience, New York, 1961. G. de Rham, Variétés différentiables, Hermann, Paris, 1955.
- Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
- K. I. Virtanen, Über die Existenz von beschränkten harmonischen Funktionen auf offenen Riemannschen Flächen, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1950 (1950), no. 75, 8 (German). MR 38443
- Shing Tung Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228. MR 431040, DOI 10.1002/cpa.3160280203
- Shing Tung Yau, Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana Univ. Math. J. 25 (1976), no. 7, 659–670. MR 417452, DOI 10.1512/iumj.1976.25.25051
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 487-490
- MSC: Primary 58A10; Secondary 58G99
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612746-9
- MathSciNet review: 612746