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Abstract and Applied Analysis
Volume 2015, Article ID 410896, 7 pages
http://dx.doi.org/10.1155/2015/410896
Research Article

Some Inequalities for the Omori-Yau Maximum Principle

Korea Institute for Advanced Study, Hoegiro 85, Seoul 130-722, Republic of Korea

Received 22 January 2015; Revised 25 June 2015; Accepted 2 July 2015

Academic Editor: Leszek Gasinski

Copyright © 2015 Kyusik Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Omori, “Isometric immersions of Riemannian manifolds,” Journal of the Mathematical Society of Japan, vol. 19, pp. 205–214, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. T. Yau, “Harmonic functions on complete Riemannian manifolds,” Communications on Pure and Applied Mathematics, vol. 28, pp. 201–228, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Q. Chen and Y. L. Xin, “A generalized maximum principle and its applications in geometry,” American Journal of Mathematics, vol. 114, no. 2, pp. 355–366, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Ratto, M. Rigoli, and A. G. Setti, “On the Omori-Yau maximum principle and its applications to differential equations and geometry,” Journal of Functional Analysis, vol. 134, no. 2, pp. 486–510, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. A. Borbély, “A remark on Omori-Yau maximum principle,” Kuwait Journal of Science, vol. 39, no. 2, pp. 45–56, 2012. View at Google Scholar
  6. G. P. Bessa, S. Pigola, and A. G. Setti, “Spectral and stochastic properties of the f-laplacian, solutions of PDEs at infinity and geometric applications,” Revista Matemática Iberoamericana, vol. 29, no. 2, pp. 579–610, 2013. View at Google Scholar
  7. H. L. Royden, “The Ahlfors-Schwarz lemma in several complex variables,” Commentarii Mathematici Helvetici, vol. 55, no. 4, pp. 547–558, 1980. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. K.-T. Kim and H. Lee, “On the Omori-Yau almost maximum principle,” Journal of Mathematical Analysis and Applications, vol. 335, no. 1, pp. 332–340, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. K. Hong and C. Sung, “An Omori-Yau maximum principle for semi-elliptic operators and Liouville-type theorems,” Differential Geometry and its Applications, vol. 31, no. 4, pp. 533–539, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. S. Pigola, M. Rigoli, and A. G. Setti, “A remark on the maximum principle and stochastic completeness,” Proceedings of the American Mathematical Society, vol. 131, no. 4, pp. 1283–1288, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Pigola, M. Rigoli, and A. G. Setti, Maximum Principles on Riemannian Manifolds and Applications, vol. 882 of Memoirs of the American Mathematical Society, American Mathematical Society, 2005.
  12. K. Takegoshi, “A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds,” Nagoya Mathematical Journal, vol. 151, pp. 25–36, 1998. View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Albanese, L. J. Alías, and M. Rigoli, “A general form of the weak maximum principle and some applications,” Revista Matemática Iberoamericana, vol. 29, no. 4, pp. 1437–1476, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. G. P. Bessa and L. F. Pessoa, “Maximum principle for semi-elliptic trace operators and geometric applications,” Bulletin of the Brazilian Mathematical Society, vol. 45, no. 2, pp. 243–265, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. Petersen, Riemannian Geometry, vol. 171 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar · View at MathSciNet