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Diastolic and isoperimetric inequalities on surfaces

Florent Balacheff, Stéphane Sabourau (2010)

Annales scientifiques de l'École Normale Supérieure

We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show that any closed Riemannian surface can be swept out by a family of multi-loops whose lengths are bounded in terms of the area of the surface. This diastolic inequality, which relies on an upper bound on Cheeger’s constant, yields an effective process to find short closed geodesics on the two-sphere, for instance. We deduce...

Diffeomorphisms constructively associated with mutually diverging spacetimes which allow a natural identification of event points in general relativity. Part II

Gaetano Zampieri (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si dà una definizione di divergenza fra cronotopi della Relatività Generale e si costruisce un criterio per l'identificazione dei punti eventi di cronotopi divergenti che appartengono ad una classe consistente con la presenza di campi elettromagnetici nel vuoto.

Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem

Bruno Franchi, Marco Marchi, Raul Paolo Serapioni (2014)

Analysis and Geometry in Metric Spaces

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally finite G-perimeter....

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