
Differential Harnack inequalities and the Ricci flow / Reto Muller
Tác giả : Reto Muller
Nhà xuất bản : European Mathematical Society
Năm xuất bản : 2006
Nơi xuất bản : Germany
Mô tả vật lý : vi, 92 p. : ill. ; 25 cm
ISBN : 3037190302
Số phân loại : 516.362
Tùng thư :
Series of lectures in mathematics
Chủ đề : 1. Hình học vi phân. 2. Global differential geometry. 3. Hình học.
Thông tin chi tiết
Tóm tắt : | In 2002, Grisha Perelman presented a new kind of differential Harnack inequality which involves both the (adjoint) linear heat equation and the Ricci flow. This led to a completely new approach to the Ricci flow that allowed interpretation as a gradient flow which maximizes different entropy functionals. The goal of this book is to explain this analytic tool in full detail for the two examples of the linear heat equation and the Ricci flow. It begins with the original Li-Yau result, presents Hamilton's Harnack inequalities for the Ricci flow, and ends with Perelman's entropy formulas and space-time geodesics. The book is a self-contained, modern introduction to the Ricci flow and the analytic methods to study it. It is primarily addressed to students who have a basic introductory knowledge of analysis and of Riemannian geometry and who are attracted to further study in geometric analysis. No previous knowledge of differential Harnack inequalities or the Ricci flow is required. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. |
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https://lrcopac.ctu.edu.vn/pages/opac/wpid-detailbib-id-134078.html |