Scalar curvature of definable Alexandrov spaces.

Bernig, Andreas

Displaying similar documents to “Scalar curvature of definable Alexandrov spaces.”

Scalar curvature of defineable CAT-spaces.

Bernig, Andreas (2003)

Advances in Geometry

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Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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In some recent work, fractal curvatures $C_{k}^{f} (F)$ and fractal curvature measures $C_{k}^{f} (F, \cdot)$ , $k = 0, ..., d$ , have been determined for all self-similar sets $F$ in $ℝ^{d}$ , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...

A rough curvature-dimension condition for metric measure spaces

Anca-Iuliana Bonciocat (2014)

Open Mathematics

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We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations...

Scalar curvature, covering spaces, and Seiberg-Witten theory.

LeBrun, Claude (2003)

The New York Journal of Mathematics [electronic only]

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Geometries of Curvature and Their Aesthetics

Brent Collins (2001)

Visual Mathematics

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Boundaries of prescribed mean curvature

Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)

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

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The existence of a singular curve in $R^{2}$ is proven, whose curvature can be extended to an $L^{2}$ function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.

Curvature contents of geometric spaces.

Lohkamp, Joachim (1998)

Documenta Mathematica

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Uniqueness results for the Minkowski problem extended to hedgehogs

Yves Martinez-Maure (2012)

Open Mathematics

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The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere $𝕊^{n}$ of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.