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A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 2. Alternative completion of Bressan's work, fit for extension to special relativity

Adriano Montanaro (1987)

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

The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- is suitable for extension to special relativity. The main reason of this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following [1], the notion of (physical) equivalence among affine inertial frames, and that of (physical isotropy of these frames are introduced; it is shown that...

A gravitational effective action on a finite triangulation as a discrete model of continuous concepts

Albert Ko, Martin Roček (2006)

Archivum Mathematicum

We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a triangulation. The variation of this function under local rescalings of the edge lengths sharing a vertex is the Euler density, and we use it to illustrate how continuous concepts can have natural discrete analogs.

A new characterization of r -stable hypersurfaces in space forms

H. F. de Lima, M. A. Velásquez (2011)

Archivum Mathematicum

In this paper we study the r -stability of closed hypersurfaces with constant r -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the r -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the r -th mean curvature.

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