Displaying similar documents to “A limiting geometry for capillary surfaces”

Doubling constant mean curvature tori in S 3

Adrian Butscher, Frank Pacard (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Clifford tori in S 3 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...

Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

Yu. Lyubich (1999)

Studia Mathematica

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For a bounded linear operator T in a Banach space the Ritt resolvent condition ∥ R λ ( T ) ∥ ≤ C / | λ - 1 | (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, a r c c o s ( C - 1 ) < δ < π / 2 . 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.