Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T00:29:25.901Z Has data issue: false hasContentIssue false
  • English
  • Français

PROPERLY EMBEDDED MINIMAL ANNULI BOUNDED BY A CONVEX CURVE

Published online by Cambridge University Press:  24 January 2003

Joaquin Pérez  and
Antonio Ros
Joaquin Pérez
Affiliation:
Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Fuentenueva, 18071 Granada, Spain (jperez@ugr.es; aros@ugr.es)
Antonio Ros
Affiliation:
Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Fuentenueva, 18071 Granada, Spain (jperez@ugr.es; aros@ugr.es)
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that given a convex Jordan curve $\varGamma\subset\{x_3=0\}$, the space of properly embedded minimal annuli in the half-space $\{x_3\geq0\}$, with boundary $\varGamma$ is diffeomorphic to the interval $[0,\infty)$. Moreover, for a fixed positive number $a$, the exterior Plateau problem that consists of finding a properly embedded minimal annulus in the upper half-space, with finite total curvature, boundary $\varGamma$ and a catenoid type end with logarithmic growth $a$ has exactly zero, one or two solutions, each one with a different stability character for the Jacobi operator.

AMS 2000 Mathematics subject classification: Primary 53A10. Secondary 49Q05; 53C42

Keywords

minimal surfacelogarithmic growthJacobi operator
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 2 , April 2002 , pp. 293 - 305
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)