Volume growth, "a priori" estimates, and geometric applications

Geometric and Functional Analysis

Volumn 13, Issue 6, 2003, Pages 1302-1328

  Pigola, Stefano ^a   Rigoli, Marco ^b   Setti, Alberto G ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF INSUBRIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1142264315     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-003-0447-2     Document Type: Article

References (23)

1. [BRS] L. BRANDOLINI, M. RIGOLI, A.G. SETTI, Positive solutions of Yamabe type equations on complete manifolds and applications, J. Funct. Anal. 160 (1998), 176-222.
2. [C] S.S. CHERN, On holomorphic mappings of Hermitian manifolds of the same dimension, Entire Functions and Related Parts of Analysis, Proc. Symp. Pure Math. 11, (1968), 157-170.
3. [EL1] J. EELLS, L. LEMAIRE, Selected Topics In Harmonic Maps, C.B.M.S. Regional Conference Ser. in Math 50. Amer. Math. Soc., Providence, R.I. 1983
4. [EL2] J. EELLS, L. LEMAIRE, Another report on harmonic maps, Bull. London Math. Soc. 20 (1998), 385-524.
5. n, Adv. Math. 118:2 (1996), 177-243.
6. [G1] A. GRIGOR'YAN, Bounded solutions of the Schrödinger equations on noncompact Riemannian manifolds (Russian) Trudy Sem. Petrovsk. 14 (1989), 66-77, 265-266; translation in J. Soviet Math. 51:3 (1990), 2340-2349.
7. [G1] A. GRIGOR'YAN, Bounded solutions of the Schrödinger equations on noncompact Riemannian manifolds (Russian) Trudy Sem. Petrovsk. 14 (1989), 66-77, 265-266; translation in J. Soviet Math. 51:3 (1990), 2340-2349.
8. [G2] A. GRIGOR'YAN, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. 36 (1999), 135-249.
9. [GK] A. GRIGOR'YAN, M. KELBERT, On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds, J. London Math. Soc. (2) 62:2 (2000), 625-639.
10. [LY] P. Li, S.T. YAU, Curvature and holomorphic mappings of complete Kähler manifolds, Compositio Math. 73 (1990), 125-144.
11. [Lu] C. Lu, Holomorphic mappings of complex manifolds, J. Diff. Geom. 2 (1968), 299-312.
12. [PS] L.A. PELETIER, J. SERRIN, Gradient bounds and Liouville theorems for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978). 65-104.
13. [PiRS1] S. PIGOLA, M. RIGOLI, A.G. SETTI, Maximum principles and singular elliptic inequalities, J. Funct. Anal. 193:2 (2002), 224-260.
14. [PiRS2] S. PIGOLA, M. RIGOLI, A.G. SETTI, Some remarks on the prescribed mean curvature equation on complete manifolds, Pacific J. Math. 206:1 (2002), 195-217.
15. [PiRS3] S. PIGOLA, M. RIGOLI, A.G. SETTI, A remark on the maximum principle and stochastic completeness, Proc. Amer. Math. Soc. 131:4 (2003), 1283-1288.
16. [PuS] P. PUCCI, J. SERRIN, A note on the strong maximum principle for elliptic differential inequalities, J. Math. Pures Appl. 79 (2000), 57-71.
17. [PuSZ] P. PUCCI, J. SERRIN, H. ZOU, A strong maximum principle and a compact support principle for singular elliptic inequalities, J. Math. Pures Appl. 78 (1999), 769-789.
18. [RRS1] A. RATTO, M. RIGOLI, A.G. SETTI, On the Omori-Yau maximum principle and its applications to differential equations and geometry, J. Func. Anal. 134 (1995), 486-510.
19. [RRS2] A. RATTO, M. RIGOLI, A.G. SETTI, A uniqueness result in PDE's and parallel mean curvature immersions in Euclidean space, Complex Variables 30 (1996), 221-233.
20. [RRV] A. RATTO, M. RIGOLI, L. VERON, Scalar curvature and conformal deformations of noncompact manifolds, Math. Z. 225 (1997), 395-426.
21. [RiS] M. RIGOLI, A.G. SETTI, Liouville-type theorems for φ-subharmonic functions, Rev. Mat. Iberoamericana, 17:3 (2001), 471-520.
22. [S1] J. SERRIN, Entire solutions of nonlinear Poisson equations, Proc. London Math. Soc. 24 (1972), 384-366.
23. [S2] J. SERRIN, On the strong maximum principle for quasilinear second order differential inequalities, J. Func. Anal. 5 (1970), 184-193.