H-surface index formula
Ruben Jakob
Mathematisches Institut der Universität, Bonn, Germany
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Abstract
We construct an additive index on the set of compact “parts” of the set of “small” H-surfaces () that are spanned into a simple closed polygon with vertices () by a combination of Heinz' and Hildebrandt's examinations of H-surfaces and Dold's fixed point theory. We obtain that the index of is always 1, independent of and . Moreover we compute that the Čech cohomology of a part that minimizes the H-surface functional locally is non-trivial at most in degrees and there even finitely generated, which implies the finiteness of the number of connected components of in particular. Finally the index of such an “-minimizing” part reveals to coincide with its Čech–Euler characteristic, which yields a variant of the mountain-pass-lemma.
Cite this article
Ruben Jakob, H-surface index formula. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 5, pp. 557–578
DOI 10.1016/J.ANIHPC.2004.10.008