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Handle addition for doubly-periodic Scherk surfaces
-
Matthias Weber
and
Michael Wolf
Published/Copyright:
December 22, 2011
Abstract
We prove the existence of a family of embedded doubly periodic minimal surfaces of (quotient) genus g with orthogonal ends that generalizes the classical doubly periodic surface of Scherk and the genus-one Scherk surface of Karcher. The proof of the family of immersed surfaces is by induction on genus, while the proof of embeddedness is by the conjugate Plateau method.
Received: 2010-08-04
Revised: 2011-01-23
Published Online: 2011-12-22
Published in Print: 2012-09
©[2012] by Walter de Gruyter Berlin Boston
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- Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem
- Are large distance Heegaard splittings generic?
- The C*-algebra of a vector bundle
- On the modular interpretation of the Nagaraj–Seshadri locus
- Handle addition for doubly-periodic Scherk surfaces
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Articles in the same Issue
- Canonical subgroups over Hilbert modular varieties
- Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem
- Are large distance Heegaard splittings generic?
- The C*-algebra of a vector bundle
- On the modular interpretation of the Nagaraj–Seshadri locus
- Handle addition for doubly-periodic Scherk surfaces
- On the resonances and eigenvalues for a 1D half-crystal with localised impurity
