کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592678 1335125 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
چکیده انگلیسی

We establish a point-wise gradient estimate for all positive solutions of the conjugate heat equation. This contrasts to Perelman's point-wise gradient estimate which works mainly for the fundamental solution rather than all solutions. Like Perelman's estimate, the most general form of our gradient estimate does not require any curvature assumption. Moreover, assuming only lower bound on the Ricci curvature, we also prove a localized gradient estimate similar to the Li–Yau estimate for the linear Schrödinger heat equation. The main difference with the linear case is that no assumptions on the derivatives of the potential (scalar curvature) are needed. A classical Harnack inequality follows.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 255, Issue 4, 15 August 2008, Pages 1008-1023