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Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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 formulations...

Curvature integral and Lipschitz parametrization in 1-regular metric spaces.

Hahlomaa, Immo (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

Curvature measures and fractals [Book]

Steffen Winter (2008)

We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.

Displaying 241 – 246 of 246

Curvature bounds for neighborhoods of self-similar sets

Curvature integral and Lipschitz parametrization in 1-regular metric spaces.

Curvature measures and fractals [Book]

Cyclic approximation of analytic cocycles over irrational rotations

Cyclic approximation of ergodic step cocycles over irrational rotations

Cyclic space isomorphism of unitary operators

Currently displaying 241 – 246 of 246