J. Perez  & A. Ros, Properly embedded minimal surfaces with finite total curvature, The Global theory of minimal surfaces in flat spaces, Lecture Notes in Math., Springer, 1775, ed. G. P. Pirola, (2002) 15-66. 


Classical theory of minimal surfaces is a beautiful and active field of research. In the paper Properly embedded minimal surfaces with finite total curvature  (63 pages, 849 Kb, Pdf file) we introduce some aspects of this theory. It is based on the lectures given by the second author at  the CIME course Minimal surfaces in flat three-manifolds organized by Gian Pietro Pirola  (Martina-Franca, Italy, summer of 1999). The other speakers were Pascal Collin, Williams Meeks and Harold Rosenberg.        

soap film experiment: non existence of certain minimal surfaces with vertical forces 

 
 

Properly embedded minimal surfaces
 with finite total curvature

by Joaquín Pérez & Antonio Ros

      Table of contents

1.  Background
Weierstrass representation
Finite total curvature
Maximum principle
Monotonicity formula
Stability
The Plateau problem		 4.  Limits of Minimal Surfaces
Minimal graphs
Sequences with uniform curvature bounds
- Bounded Area
- Unbounded Area
Sequences with total curvature bounds
- Limits in open domains
- Limits in R^3
2.  Minimal Surfaces with Vertical Forces I
Basic properties of forces
- Vertical forces
- The deformation
A characterization of the Catenoid
Other results on vertical forces
- A property of planar ends
- Singly periodic minimal surfaces


5.  Compactness of the Moduli Space of Minimal Surfaces
Weak Compactness
Strong Compactness

3. Minimal Surfaces with Vertical Forces II
Immersed 3-manifolds
Topological uniqueness
Related results

  

 

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