Weighted Poincaré inequality and rigidity of complete manifolds

Peter Li; Jiaping Wang

Annales scientifiques de l'École Normale Supérieure (2006)

  • Volume: 39, Issue: 6, page 921-982
  • ISSN: 0012-9593

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Li, Peter, and Wang, Jiaping. "Weighted Poincaré inequality and rigidity of complete manifolds." Annales scientifiques de l'École Normale Supérieure 39.6 (2006): 921-982. <http://eudml.org/doc/82704>.

@article{Li2006,
author = {Li, Peter, Wang, Jiaping},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {weighted Poincaré inequality; complete manifolds; Ricci curvature},
language = {eng},
number = {6},
pages = {921-982},
publisher = {Elsevier},
title = {Weighted Poincaré inequality and rigidity of complete manifolds},
url = {http://eudml.org/doc/82704},
volume = {39},
year = {2006},
}

TY - JOUR
AU - Li, Peter
AU - Wang, Jiaping
TI - Weighted Poincaré inequality and rigidity of complete manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2006
PB - Elsevier
VL - 39
IS - 6
SP - 921
EP - 982
LA - eng
KW - weighted Poincaré inequality; complete manifolds; Ricci curvature
UR - http://eudml.org/doc/82704
ER -

References

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  1. [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. Zbl0503.35001MR745286
  2. [2] Cai M., Galloway G.J., Boundaries of zero scalar curvature in the ADS/CFT correspondence, Adv. Theor. Math. Phys.3 (1999) 1769-1783. Zbl0978.53084MR1812136
  3. [3] Cao H., Shen Y., Zhu S., The structure of stable minimal hypersurfaces in R n + 1 , Math. Res. Lett.4 (1997) 637-644. Zbl0906.53004MR1484695
  4. [4] Cheng S.Y., Yau S.T., Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math.28 (1975) 333-354. Zbl0312.53031MR385749
  5. [5] Fefferman C., Phong D.H., The uncertainty principle and sharp Gårding inequalities, Comm. Pure Appl. Math.34 (1981) 285-331. Zbl0458.35099MR611747
  6. [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. Zbl0492.35057MR672274
  7. [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. Zbl0822.58001MR1320504
  8. [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. Zbl1066.53084MR1919432
  9. [9] Li P., Tam L.F., Complete surfaces with finite total curvature, J. Diff. Geom.33 (1991) 139-168. Zbl0749.53025MR1085138
  10. [10] Li P., Tam L.F., Harmonic functions and the structure of complete manifolds, J. Diff. Geom.35 (1992) 359-383. Zbl0768.53018MR1158340
  11. [11] Li P., Wang J., Complete manifolds with positive spectrum, J. Diff. Geom.58 (2001) 501-534. Zbl1032.58016MR1906784
  12. [12] Li P., Wang J., Complete manifolds with positive spectrum, II, J. Diff. Geom.62 (2002) 143-162. Zbl1073.58023MR1987380
  13. [13] Li P., Wang J., Comparison theorem for Kähler manifolds and positivity of spectrum, J. Diff. Geom.69 (2005) 43-74. Zbl1087.53067MR2169582
  14. [14] Nakai M., On Evans potential, Proc. Japan Acad.38 (1962) 624-629. Zbl0197.08604MR150296
  15. [15] Napier T., Ramachandran M., Structure theorems for complete Kähler manifolds and applications to Lefschetz type theorems, Geom. Funct. Anal.5 (1995) 809-851. Zbl0860.53045MR1354291
  16. [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. Zbl0361.53040MR438388
  17. [17] Schoen R., Yau S.T., Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math.92 (1988) 47-71. Zbl0658.53038MR931204
  18. [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. Zbl0558.31009MR730112
  19. [19] Wang X., On conformally compact Einstein manifolds, Math. Res. Lett.8 (2001) 671-688. Zbl1053.53030MR1879811
  20. [20] Witten E., Yau S.T., Connectness of the boundary in the ADS.CFT correspondence, Adv. Theor. Math. Phys.3 (1999) 1635-1655. Zbl0978.53085MR1812133
  21. [21] Yau S.T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math.28 (1975) 201-228. Zbl0291.31002MR431040
  22. [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. Zbl0335.53041MR417452

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