scholarly journals Self-dual centroaffine surfaces of codimension two with constant affine mean curvature

2002 ◽  
Vol 9 (4) ◽  
pp. 573-587
Author(s):  
Hitoshi Furuhata ◽  
Takashi Kurose
Keyword(s):  
Mean Curvature ◽  
Codimension Two ◽  
Affine Mean Curvature ◽  
Constant Affine Mean Curvature

Regularity results for solutions to the c-Plateau problem with free boundary having small singular set, and generally in codimension zero

2016 ◽  
Vol 9 (3) ◽  
pp. 259-282 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Free Boundary ◽  
Minimization Problem ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Plateau Problem ◽  
Singular Set ◽  
Codimension Two ◽  
Rectifiable Currents ◽  
Problem With Free Boundary ◽  
Regularity Results

AbstractWe prove two results for the c-Plateau problem, introduced in [17], which is a minimization problem for integer rectifiable currents. First, we prove there is no solution to the c-Plateau problem with free boundary having singular set of finite Hausdorff codimension two measure and with regular part having constant mean curvature. Second, we prove regularity up to Hausdorff codimension seven of the free boundary of top-dimensional solutions to the c-Plateau problem.

Sign in / Sign up

Export Citation Format

Share Document