Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung
In: manuscripta mathematica, Jg. 40 (1982-02-01), Heft 1, S. 1-15
Online
serialPeriodical
Zugriff:
In the Sobolev space H m (B,R 3 ), B the open unit disc in R 2 , we consider the set M n of all conformally parametrized surfaces of constant mean curvature H with exactly n simple interior branch points (and no others). We denote by M* n the set of all xeM n with the following properties:i)in every branch point the geometrical condition K G ¦x Z ¦=O holds (K G is the Gauss curvature and x z is the complex gradient of the surface x).ii)the corresponding boundary value problem ?h+× z { 2 (2H 2 -K G )h=O, h δB=O, is uniquely solvable.We prove then, that the manifold M*=UM* n is open and dense in the set of all surfaces of constant mean curvature H and that all x eM* n are isolated and stable solutions of the Plateau problem corresponding to their boundary curves. In addition, the submanifold M* n contains exactly all surfaces x for which the space of Jacobi fields is transversal (with exception of the 3-dimensional space of conformai directions) to the tangent space T x M n .
Titel: |
Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung
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Autor/in / Beteiligte Person: | Schüffler, Karlheinz |
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Zeitschrift: | manuscripta mathematica, Jg. 40 (1982-02-01), Heft 1, S. 1-15 |
Veröffentlichung: | 1982 |
Medientyp: | serialPeriodical |
ISSN: | 0025-2611 (print) ; 1432-1785 (print) |
DOI: | 10.1007/BF01168233 |
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