Geodesic nets on the 2-sphere

Author:

Hass Joel,Morgan Frank

Abstract

In this paper we introduce the concept of a geodesic net, an idea which plays the role among graphs that geodesics play among simple closed curves. We establish the existence of specific geodesic nets on the 2-sphere in certain cases.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference11 articles.

1. [A-T] F. J. Almgren, Jr., and Jean E. Taylor, The geometry of soap films and soap bubbles, Scientific American, July, 1976, 82–93.

2. On the existence and regularity of fundamental domains with least boundary area;Choe, Jaigyoung;J. Differential Geom.,1989

3. Poincaré’s problem and the length of the shortest closed geodesic on a convex hypersurface;Croke, Christopher B.;J. Differential Geometry,1982

4. Shortening embedded curves;Grayson, Matthew A.;Ann. of Math. (2),1989

5. [H-M] J. Hass and F. Morgan, Geodesics and soap bubbles on surfaces (Math. Z., to appear).

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