Absolute gradient bound for surfaces of constant mean curvature
Kok Seng Chua (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Kok Seng Chua (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Robert Finn, Enrico Giusti (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Michele Emmer (1981)
Rendiconti del Seminario Matematico della Università di Padova
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Enrico Giusti (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Adrian Butscher, Frank Pacard (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The Clifford tori in constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled...
Yu. Lyubich (1999)
Studia Mathematica
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For a bounded linear operator T in a Banach space the Ritt resolvent condition (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, . This implies the power boundedness of the operator T. A key result is that the spectrum σ(T) is contained in a special convex closed domain. A generalized Ritt condition leads to a similar localization result and then to a theorem on invariant subspaces.