Výsledky vyhledávání - "KOELLER, AMOS"

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Minkowski and packing Dimension comparisons for sets with Reifenberg properties

Autor: Koeller, Amos N.

In Koeller \cite{koerprops} the twelve variants of the Reifenberg properties known to be instrumental in the theory of minimal surfaces were classified with respect to various Hausdorff measure based measure theoretic properties. The classification l

Externí odkaz: http://arxiv.org/abs/1101.3596

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Outer measure preserving ergodic transformations generate the Carath\'eodory definition of measurable sets

Autor: Koeller, Amos N.

It is known that there are specific examples of ergodic transformations on measure spaces for which the calculation of the outer measure of transformation invariant sets leads to a condition closely resembling Carath\'eodory's condition for sets to b

Externí odkaz: http://arxiv.org/abs/1101.1532

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A classification of Reifenberg properties

Autor: Koeller, Amos N.

We define twelve variants of a Reifenberg's affine approximation property, which are known to be connected with the singular sets of minimal surfaces. With this motivation we investigate the regularity of the sets possessing these. We classify the pr

Externí odkaz: http://arxiv.org/abs/1012.4275

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On the singular set of mean curvature flows with Neumann free boundary conditions

Autor: Koeller, Amos N.

We consider $n$-dimensional hypersurfaces flowing by mean curvature flow with Neumann free boundary conditions supported on a smooth support surface. We show that the Hausdorff $n$-measure of the singular set is zero. In fact, we consider two types o

Externí odkaz: http://arxiv.org/abs/1012.0601

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Evolution of convex lens-shaped networks under curve shortening flow

Autor: Schnürer, Oliver C., Azouani, Abderrahim, Georgi, Marc, Hell, Juliette, Jangle, Nihar, Koeller, Amos, Marxen, Tobias, Ritthaler, Sandra, Sáez, Mariel, Schulze, Felix, Smith, Brian

We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a

Externí odkaz: http://arxiv.org/abs/0711.1108

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Approximately j-dimensional Koch type sets are potentially minimal surfaces

Autor: Koeller, Amos N.

We investigate the approximate j-dimensionality of the singularity sets of minimal surfaces prescribed by Simon. This leads to the clasification of 8 variations of approximately j-dimensional surfacs in terms of dimension and locally finite Hausdorff

Externí odkaz: http://arxiv.org/abs/math/0608528

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