Weighted Poincaré inequality and rigidity of complete manifolds

Li, Peter; Wang, Jiaping

doi:10.1016/j.ansens.2006.11.001

Li, Peter ; Wang, Jiaping

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 6, pp. 921-982.

MR Zbl | 3 citations dans Numdam

DOI : 10.1016/j.ansens.2006.11.001

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     author = {Li, Peter and Wang, Jiaping},
     title = {Weighted {Poincar\'e} inequality and rigidity of complete manifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {921--982},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {6},
     year = {2006},
     doi = {10.1016/j.ansens.2006.11.001},
     mrnumber = {2316978},
     zbl = {05149414},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2006.11.001/}
}

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Li, Peter; Wang, Jiaping. Weighted Poincaré inequality and rigidity of complete manifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 6, pp. 921-982. doi : 10.1016/j.ansens.2006.11.001. http://www.numdam.org/articles/10.1016/j.ansens.2006.11.001/

Bibliographie
Cité par

[1] Agmon S., Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrödinger Operators, Mathematical Notes, vol. 29, Princeton University Press, Princeton, NJ, 1982. | MR | Zbl

[2] Cai M., Galloway G.J., Boundaries of zero scalar curvature in the ADS/CFT correspondence, Adv. Theor. Math. Phys. 3 (1999) 1769-1783. | MR | Zbl

[3] Cao H., Shen Y., Zhu S., The structure of stable minimal hypersurfaces in $R^{n + 1}$ , Math. Res. Lett. 4 (1997) 637-644. | MR | Zbl

[4] Cheng S.Y., Yau S.T., Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975) 333-354. | MR | Zbl

[5] Fefferman C., Phong D.H., The uncertainty principle and sharp Gårding inequalities, Comm. Pure Appl. Math. 34 (1981) 285-331. | MR | Zbl

[6] Fefferman C., Phong D.H., Lower bounds for Schrödinger equations, in: Conference on Partial Differential Equations (Saint Jean de Monts, 1982), Conf. No. 7, Soc. Math. France, Paris, 1982, 7 pp. | Numdam | MR | Zbl

[7] Li P., Lecture Notes on Geometric Analysis, Lecture Notes Series, vol. 6, Research Institute of Mathematics and Global Analysis Research Center, Seoul National University, Seoul, 1993. | MR | Zbl

[8] Li P., Curvature and function theory on Riemannian manifolds, in: Surveys in Differential Geometry: Papers Dedicated to Atiyah, Bott, Hirzebruch, and Singer, vol. VII, International Press, Cambridge, 2000, pp. 375-432. | MR | Zbl

[9] Li P., Tam L.F., Complete surfaces with finite total curvature, J. Diff. Geom. 33 (1991) 139-168. | MR | Zbl

[10] Li P., Tam L.F., Harmonic functions and the structure of complete manifolds, J. Diff. Geom. 35 (1992) 359-383. | MR | Zbl

[11] Li P., Wang J., Complete manifolds with positive spectrum, J. Diff. Geom. 58 (2001) 501-534. | MR | Zbl

[12] Li P., Wang J., Complete manifolds with positive spectrum, II, J. Diff. Geom. 62 (2002) 143-162. | MR | Zbl

[13] Li P., Wang J., Comparison theorem for Kähler manifolds and positivity of spectrum, J. Diff. Geom. 69 (2005) 43-74. | MR | Zbl

[14] Nakai M., On Evans potential, Proc. Japan Acad. 38 (1962) 624-629. | MR | Zbl

[15] Napier T., Ramachandran M., Structure theorems for complete Kähler manifolds and applications to Lefschetz type theorems, Geom. Funct. Anal. 5 (1995) 809-851. | MR | Zbl

[16] Schoen R., Yau S.T., Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature, Comm. Math. Helv. 39 (1981) 333-341. | MR | Zbl

[17] Schoen R., Yau S.T., Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988) 47-71. | MR | Zbl

[18] Varopoulos N., Potential theory and diffusion on Riemannian manifolds, in: Conference on Harmonic Analysis in Honor of Antoni Zygmund, vols. I, II, Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 821-837. | MR | Zbl

[19] Wang X., On conformally compact Einstein manifolds, Math. Res. Lett. 8 (2001) 671-688. | MR | Zbl

[20] Witten E., Yau S.T., Connectness of the boundary in the ADS.CFT correspondence, Adv. Theor. Math. Phys. 3 (1999) 1635-1655. | MR | Zbl

[21] Yau S.T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975) 201-228. | MR | Zbl

[22] Yau S.T., Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana Univ. Math. J. 25 (1976) 659-670. | MR | Zbl

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