中国综合性科技类核心期刊(北大核心)

中国科学引文数据库来源期刊(CSCD)

美国《化学文摘》(CA)收录

美国《数学评论》(MR)收录

俄罗斯《文摘杂志》收录

Message Board

Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review, editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!

Name
E-mail
Phone
Title
Content
Verification Code
Issue 4
Dec.  2014
Turn off MathJax
Article Contents
WANG Jian-Hong. Harnack estimate for the Schrodinger equation under Ricci flow[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 36-42.
Citation: WANG Jian-Hong. Harnack estimate for the Schrodinger equation under Ricci flow[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 36-42.

Harnack estimate for the Schrodinger equation under Ricci flow

  • Received Date: 2011-06-01
  • Rev Recd Date: 2011-09-01
  • Publish Date: 2012-07-25
  • This paper established the gradient estimate and Harnack inequalities of the Schrodinger equation when the metric is evolved by Ricci flow, and extended the results ofthe heat equation by C.M.Guenther
  • loading
  • [1] CHENG S Y, YAU S T. Differential equations on Riemannianmanifold and their applications[J]. Communications on Pure and Applied Mathematics, 1975, 28(3): 333-354.

    [2] HAMILTION R S. A matrix Harnack estimate for the heat equation[J]. Comm Anal Geom, 1993, 1(1): 113-126.

    [3] LI P, YAU S T. On the parabolic kernel of the Schrodinger operator[J]. Acta Math, 1986, 156(3-4): 153-201.

    [4] HAMILTION R S. The Harnack estimate for the Ricci flow[J]. J Differential Geometry, 1993, 37(1): 225-243.

    [5] HAMILTION R S. The Ricci flow on surfaces[J]. Mathematics and General Relativity, 1988, 71(1): 237-262.

    [6] CHOW B. The Ricci flow on the 2-sphere[J]. J Differential Geometry, 1991, 33(2): 325-334.

    [7] HAMILTION R S. Harnack estimate for the mean curvature flow[J]. J Differential Geometry, 1995, 41(1): 215-226.

    [8] CHOW B. On Harnack’s inequality and entropy for the Gaussian curvature flow[J]. Communications on Pure and Applied Mathematics, 1991, 44(4): 469-483.

    [9] CHOW B. The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature[J]. Communications on Pure and Applied Mathematics, 1992, 45(8): 1003-1014.

    [10] CAO H D. On Harnack inequalities for the Kahler-Ricci flow[J]. Inventiones Mathematics, 1992, 109(2): 247-263.

    [11] HAMILTION R S. Three-manifolds with positive Ricci curvature[J].J Differential Geometry, 1982, 17(2): 255-306.

    [12] CAO X D, HAMILTION R S. Differential Harnack estimates for time-dependent heat equation with potentials[J/OL]. arXiv.org/math.DG/0807.0568v1, 2008.

    [13] GUENTHE C M. The fundamental solution on manifolds with time-dependent metrics[J]. Journal of Geometric Analysis, 2002, 12(3): 425-436.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views (2371) PDF downloads(2096) Cited by()
    Proportional views

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return