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Omori-Yau maximum principle on Alexandrov spaces

이한진
대한수학회 (The Korean Mathematical Society)|2016.05|대한수학회지 (Journal of the KMS)|제53권 제3호|pp. 533-547

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키워드

Omori-Yau maximum principleAlexandrov spaceBishop-Gromov condition
주제분류수학

초록

We prove an Omori-Yau maximum principle on Alexandrov spaces which do not have Perelman singular points and satisfy the infinitesimal Bishop-Gromov condition.

Abstract

We prove an Omori-Yau maximum principle on Alexandrov spaces which do not have Perelman singular points and satisfy the infinitesimal Bishop-Gromov condition.

참고문헌 (20)

  1. L. Ambrosio, "Functions of Bounded Variation and Free Discontinuity Problems" (2000), Oxford University Press
  2. L. Ambrosio, "Rectifiable sets in metric and Banach spaces", Math. Ann, 318(3), pp.527~555 (2000)
  3. D. Burago, "A Course in Metric Geometry, Graduate Studies in Mathematics", American Mathematical Society, 33 (2001)
  4. Y. Burago, "A. D. Aleksandrov spaces with curvature bounded below", Russian Math. Surveys, 47(2), pp.1~58 (1992)
  5. K. Kuwae, "Sobolev sapces, Laplacian, and heat kernel on Alexandrov spaces", Math. Z, 238(2), pp.269~316 (2001)
  6. K. Kuwae, "Laplacian comparison for Alexandrov spaces", arXiv:0709.0788, ~ (2007)
  7. K. Kuwae, "Infinitesimal Bishop-Gromov condition for Alexandrov spaces, Probabilistic approach to geometry", Adv. Stud. Pure Math, 57, pp.293~302 (2010)
  8. K. Kuwae, "A topological splitting theorem for weighted Alexandrov spaces", Tohoku Math. J, 63(1), pp.59~76 (2011)
  9. S. Ohta, "On the measure contraction property of metric measure spaces", Comment. Math. Helv, 82(4), pp.805~828 (2007)
  10. H. Omori, "Isometric immersions of Riemannian manifolds", J. Math. Soc. Japan, 19, pp.205~214 (1967)
  11. Y. Otsu, "The Riemannian structure of Alexandrov spaces", J. Differential Geom, 39(3), pp.629~658 (1994)
  12. G. Perelman, "DC-structure on Alexandrov spaces", ~
  13. A. Petrunin, "Alexandrov meets Lott-Villani-Sturm", M¨unster J. Math, 4, pp.53~64 (2011)
  14. S. Pigola, "A remark on the maximum principle and stochastic completeness", Proc. Amer. Math. Soc, 131(4), pp.1283~1288 (2003)
  15. J. Rataj, "Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces", Houston J. Math, 38(2), pp.445~467 (2012)
  16. A. Ratto, "On the Omori-Yau maximum principle and its application to differential equations and geometry", J. Funct. Anal, 134(2), pp.486~510 (1995)
  17. M.-K. von Renesse, "Heat kernel comparison on Alexandrov spaces with curvature bounded below", Potential Anal, 21(2), pp.151~176 (2004)
  18. S. T. Yau, "Harmonic functions on complete Riemannian manifolds", Comm. Pure Appl. Math, 28, pp.201~228 (1975)
  19. S. T. Yau, "A general Schwarz lemma for Kahler manifolds", Amer. J. Math, 100(1), pp.197~203 (1978)
  20. H. Zhang, "Ricci curvature on Alexandrov spaces and rigidity theorems", Comm. Anal. Geom, 18(3), pp.503~553 (2010)

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