Geodesic
Harmonic functions on Alexandrov spaces and their applications
Petrunin, Anton1
1Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 135-141

Voir la notice de l'article provenant de la source American Mathematical Society

DOI

The main result can be stated roughly as follows: Let $M$ be an Alexandrov space, $\Omega \subset M$ an open domain and $f:\Omega \to \mathbb {R}$ a harmonic function. Then $f$ is Lipschitz on any compact subset of $\Omega$. Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.
DOI : 10.1090/S1079-6762-03-00120-3

Petrunin, Anton  1

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
Petrunin, Anton. Harmonic functions on Alexandrov spaces and their applications. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 135-141. doi: 10.1090/S1079-6762-03-00120-3
@article{10_1090_S1079_6762_03_00120_3,
     author = {Petrunin, Anton},
     title = {Harmonic functions on {Alexandrov} spaces and their applications},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {135--141},
     year = {2003},
     volume = {09},
     doi = {10.1090/S1079-6762-03-00120-3},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00120-3/}
}
TY  - JOUR
AU  - Petrunin, Anton
TI  - Harmonic functions on Alexandrov spaces and their applications
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2003
SP  - 135
EP  - 141
VL  - 09
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00120-3/
DO  - 10.1090/S1079-6762-03-00120-3
ID  - 10_1090_S1079_6762_03_00120_3
ER  - 
%0 Journal Article
%A Petrunin, Anton
%T Harmonic functions on Alexandrov spaces and their applications
%J Electronic research announcements of the American Mathematical Society
%D 2003
%P 135-141
%V 09
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00120-3/
%R 10.1090/S1079-6762-03-00120-3
%F 10_1090_S1079_6762_03_00120_3

[1] Almgren, F. J., Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints Mem. Amer. Math. Soc. 1976

[2] Burago, Yu., Gromov, M., Perel′Man, G. A. D. Aleksandrov spaces with curvatures bounded below Uspekhi Mat. Nauk 1992

[3] Federer, Herbert Geometric measure theory 1969

[4] Milman, Vitali D., Schechtman, Gideon Asymptotic theory of finite-dimensional normed spaces 1986

[5] Ladyzhenskaya, O. A., Ural′Tseva, N. N. Lineĭnye i kvazilineĭnye uravneniya èllipticheskogo tipa 1973 576

[6] Kuwae, Kazuhiro, Machigashira, Yoshiroh, Shioya, Takashi Beginning of analysis on Alexandrov spaces 2000 275 284

[7] Kuwae, Kazuhiro, Machigashira, Yoshiroh, Shioya, Takashi Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces Math. Z. 2001 269 316

[8] Nikolaev, I. G. Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov Sibirsk. Mat. Zh. 1983 114 132

[9] Perel′Man, G. Ya., Petrunin, A. M. Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem Algebra i Analiz 1993 242 256

[10] Petrunin, A. Parallel transportation for Alexandrov space with curvature bounded below Geom. Funct. Anal. 1998 123 148

[11] Reshetnyak, Yu. G. Two-dimensional manifolds of bounded curvature 1989

Cité par Sources :