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Course Descriptions

16:640:519 - Selected Topics in Differential Equations

Sagun Chanillo

Subtitle:

Topics in Minimal Surfaces

Text: 

No text book, though R. Osserman's book, in Dover Press is good for some topics

Prerequisites: 

Real analysis, undergraduate differential geometry

Description: 

This course will be an introduction to minimal surfaces, which are naively area minimizing hypersurfaces. This is usually called soap film geometry. I shall cover, the (1) first variational formula for area for a surface, (2)Weierstrass representation and construction of minimal surfaces, (3) monotonicity formula, (4) Bernstein's theorem that a complete minimal graph has to be a flat plane, (5) The Gauss map, if the Gauss map of a complete minimal surface omits 9 points on S^2, then it is a flat plane (6) Plateau problem (7) Second variational formula and stability of minimal surfaces theorem of R. Schoen and Fischer-Colbrie, Do Carmo and Peng that a complete, stable minimal surface is a flat plane (8) Curvature estimates of Heinz and its generalization by Schoen-Simon-Yau (9) Morse theory of constant mean curvature surfaces the paper of Chanillo-Malchiodi, Comm. in Analysis and Geometry 13(1) (2005) 187-251.


Schedule of Sections:

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530