Counting massive sets and dimensions of harmonic functions

Journal of Differential Geometry

Volumn 53, Issue 2, 1999, Pages 237-278

  Li, Peter ^a,b   Wang, Jiaping ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012710939     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214425536     Document Type: Article

References (25)

1. R. Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981) 581-598.
2. J. Cheeger, T. Colding & W. Minicozzi, Linear growth harmonic functions on complete manifolds with non-negative Ricci curvature, Geom. Funct. Anal. 5 (1995) 948-954.
3. S. Y. Cheng, Liouville theorem for harmonic maps, Geometry of the Laplace operator, Proc. Symp. Pure Math. Amer. Math. Soc. 36 (1980) 147-151.
4. S. Y. Cheng & P. Li, Heat kernel estimates and lower bound of eigenvalues, Comment. Math. Helv. 56 (1981) 327-338.
5. T. Colding & W. Minicozzi, Weyl type bounds for harmonic functions, Invent. Math. 131 (1998) 257-298.
6. A. Grigor’yan, On the dimension of spaces of harmonic functions, Math. Notes 48 (1990) 1114-1118.
7. Z. Han, L. F. Tam, A. Treibergs & T. Wan, Harmonic maps from the complex plane into surfaces with nonpositive curvature, Comm. Anal. Geom. 3 (1995) 85-114.
8. A. Kasue, Harmonic functions with growth conditions on a manifold of asymptotically non-negative curvature. II, Recent Topics in Differential and Anal. Geom., Adv. Stud. Pure Math. Vol. 18, North-Holland, 1989.
9. A. Kasue, A compactification of a manifold with asymptotically nonnegative curvature, Ann. Sci. École Norm. Sup. 21 (1988) 593-622.
10. Y. Kifer, Bounded harmonic functions on nonamenable covers of compact manifolds, Israel J. Math. 61 (1988) 170-178.
11. F. Larusson, The Martin boundary action of Gromov hyperbolic covering groups and applications to Hardy classes, Internat. J. Math. 6 (1995) 601-624.
12. P. Li, Harmonic functions of linear growth on Kähler manifolds with non-negative Ricci curvature, Math. Res. Letters 2 (1995) 79-94.
13. P. Li, Harmonic sections of polynomial growth, Math. Research Letters 4 (1997) 35-44.
14. P. Li, Curvature and function theory on Riemannian manifolds, Survey in Differential Geom., To appear.
15. P. Li & L. F. Tam, Linear growth harmonic functions on a complete manifold, J. Differential Geom. 29 (1989) 421-425.
16. P. Li & L. F. Tam, Complete surfaces with finite total curvature, J. Differential Geom. 33 (1991) 139-168.
17. P. Li & L. F. Tam, Green’s functions, harmonic functions, and volume comparison, J. Differential Geom. 41 (1995) 277-318.
18. P. Li & J. P. Wang, Convex hull properties of harmonic maps, J. Differential Geom. 48 (1998) 497-530.
19. P. Li & J. P. Wang, Mean value inequalities, Indiana Math. J. 48 (1999) 1257-1283.
20. T. J. Lyons & D. Sullivan, Function theory, random paths and covering spaces, J. Differential Geom. 19 (1984) 299-323.
21. C. J. Sung, L. F. Tam & J. P. Wang, Spaces of harmonic functions, J. London Math. Soc., To appear.
22. L. F. Tam & T. Wan, Harmonic diffeomorphisms into Cartan-Hadamard surfaces with prescribed Hopf differentials, Comm. Anal. Geom. 2 (1995) 593-625.
23. D. Toledo, Bounded harmonic functions on coverings, Proc. Amer. Math. Soc. 104 (1988) 1218-1219.
24. T. Wan, Constant mean curvature surface, harmonic maps, and universal Te-ichmüller space, J. Differential Geom. 35 (1992) 643-657.
25. S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975) 201-228.