본문 바로가기
KERD
논문KCI 등재

Harnack Estimate for Positive Solutions to a Nonlinear Equation Under Geometric Flow

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds. We shall get an interesting Harnack inequality as an application.

Abstract

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds. We shall get an interesting Harnack inequality as an application.

참고문헌 (10)

  1. T. Aubin, "Nonlinear Analysis on Manifolds. Monge-Ampre equations" (1982), Springer
  2. E. Calabi, "An extension of E. Hopf s maximum principle with an application to Riemannian geometry", Duke Math. J, 25(1), pp.45~56 (1958)
  3. B. Chow, "The Ricci flow; An introduction" (2004), AMS
  4. R. S. Hamilton, "The Harnack estimate for the Ricci flow", J. Differ. Geom, 37(1), pp.225~243 (1993)
  5. S. Kuang, "A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow", J. Funct. Anal, 255(4), pp.1008~1023 (2008)
  6. P. Li, "On the parabolic kernel of the Schr¨odinger operator", Acta Math, 156(3-4), pp.153~201 (1986)
  7. S. P. Liu, "Gradient estimates for solutions of the heat equation under Ricci flow", Pacific J. Math, 243(1), pp.165~180 (2009)
  8. G. Perelman, "The entropy formula for the Ricci flow and its geometric applications", arXiv: math, 2002
  9. J. Sun, "Gradient estimates for positive solutions of the heat equation under geometric flow", Pacific J. Math, 253(2), pp.489~510 (2011)
  10. J. Y. Wu, "Gradient estimates for a nonlinear parabolic equation and Liouville theorems", Manuscripta mathematica, 159(3-4), pp.511~547 (2019)

관련 논문AI추천

이 간행물의 다른 논문 (14건)