Cornell Math - MATH 762, Spring 1999

MATH 762 — Spring 1999
Seminar in Geometry

Instructor: José F. Escobar

Time:  TR 10:10-11:25

Room: WE B25

This will be a course in geometric partial differential equations. Since most of the problems that appear in geometry are of variational nature, I will expend the first part of the course studying calculus of variations. I will cover chapter 8 of the book Partial Differential Equations by Craig Evans and probably a little more. Then I will study Schauder estimates for elliptic operators. I will go over the new proof of the main Schauder estimate given by Leon Simon which simplies and clarifies the old one. Then I will discuss the Hodge Theory for the Laplace operator on differential forms. In this part I will follow some recent notes by R. Schoen. If time permits, I will study some specific equations, (depending on the interest of the audience), that appear in Riemannian geometry.

A background in Riemannian geometry is not needed for this course.

A graduate course in partial differential equations is recommended.