Math 257A-topics on differential geometry
Spring, 2011
Course Description
Parabolic PDE, besides its connection with physics, probability,
applied mathematics, has been a very effective tools in solving
problems in geometric analysis. In this course we plan to cover
several important old and recent progresses in geometric evolution
equations. The topics include Weyl's asymptotics on eigenvalues via
heat kernel, Andrews-Clutterbuck's recent parabolic approach on the
fundamental gap conjecture, new parabolic proof on Li-Yau-Zhong-Yang's
eigenvalue estimate, dimension estimates of the spaces of holomorphic
functions of polynomial growth, etc. The underline theme is various
important estimates on the gradient and continuity modulus of
solutions to the parabolic equations. The nonlinear geometric PDEs
such as the mean curvature flow and Ricci flow will also be
introduced. Even though we shall start with the maximum principle and
other basics on parabolic PDE, we will cover the most recent
development and the very current technology of the subject.
There will be no final exam.
The complete course schedule will be available.
Instructors
| Name |
Office |
E-mail |
Phone |
Office Hours |
| Ni, Lei |
AP&M 5250 |
lni@math.ucsd.edu |
534-2704 |
MWF 11:00-11:50am |
|
Course Time and Location
| Section |
Instructor |
Time |
Place |
| A00 |
Ni |
MWF 10:00-10:50 am |
APM 5829 |
|
Texts
Text: (1) Linear and quasilinear equations of parabolic type, O.A. Ladyzenskaya, V. A. Solonnikov and N. N. Uralceva; (not required)
(2) Partial differential equations of parabolic type, A. Friedman; (not required)
(3) Hamilton's Ricci flow, B. Chow, P. Lu and L. Ni. (not required)
Exams
There will be no exam.
Handout
Tauberian Theorem
Schedule
The course schedule will be available.
Grades
Grades will be based on the following percentages.
Last modified: Wed July 29, 14:49:08 PST 2009