Zobrazeno 1 - 10
of 68
pro vyhledávání: '"de Pauw, Thierry"'
Autor:
Bouafia, Philippe, De Pauw, Thierry
A function $f$ defined on $[0, 1]^d$ is called strongly chargeable if there is a continuous vector-field $v$ such that $f(x_1, \dots,x_d)$ equals the flux of $v$ through the rectangle $[0, x_1] \times \cdots \times [0, x_d]$ for all $(x_1, \dots, x_d
Externí odkaz:
http://arxiv.org/abs/2401.15427
Autor:
Bouafia, Philippe, De Pauw, Thierry
Publikováno v:
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXV (2024), 483-493
We give an integral representation formula for members of the dual of $SBV(\mathbb{R}^n)$ in terms of functions that are defined on $\hat{\mathbb{R}}^n$, an appropriate fiber space that we introduce, consisting of pairs $(x,[E]_x)$ where $[E]_x$ is a
Externí odkaz:
http://arxiv.org/abs/2110.04747
Autor:
Bouafia, Philippe, De Pauw, Thierry
We study measurable spaces equipped with a $\sigma$-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version -- a kind of fiber space that describes locally their directions -- defined by a universa
Externí odkaz:
http://arxiv.org/abs/2105.11331
Autor:
De Pauw, Thierry
Letting $A \subset \mathbb{R}^n$ be Borel measurable and $W_0 : A \to \mathbb{G}(n,m)$ Lipschitzian, we establish that \begin{equation*} \limsup_{r \to 0^+} \frac{\mathcal{H}^m \left[ A \cap B(x,r) \cap (x+ W_0(x))\right]}{\alpha(m)r^m} \geq \frac{1}
Externí odkaz:
http://arxiv.org/abs/2104.04730
Autor:
De Pauw, Thierry, Hardt, Robert
The isoperimetric inequality for a smooth compact Riemannian manifold $A$ provides a positive ${\bf c}(A)$, so that for any $k+1$ dimensional integral current $S_0$ in $A$ there exists an integral current $ S$ in $A$ with $\partial S=\partial S_0$ an
Externí odkaz:
http://arxiv.org/abs/2012.02667
Autor:
De Pauw, Thierry
We characterize measure spaces such that the canonical map $L_\infty \to L_1^*$ is surjective. In case of $d$ dimensional Hausdorff measure of a complete separable metric space $X$ we give two equivalent conditions. One is in terms of the order compl
Externí odkaz:
http://arxiv.org/abs/1909.10190
Autor:
De Pauw, Thierry
Letting A be a Borel subset of n dimensional Euclidean space, and W(x) be an m dimensional affine subspace containing x and varying in a Lipschitz way according to x, we establish that A is Lebesgue null if and only if $A \cap W(x)$ has m dimensional
Externí odkaz:
http://arxiv.org/abs/1904.12276
Autor:
De Pauw, Thierry, Vasilyev, Ioann
Publikováno v:
Annales de l'Institut Fourier, Volume 73 (2023) no. 2, pp. 635-694
We introduce the notion of density contractor of dimension m in a finite dimensional normed space X. If m+1=dim X this includes the area contracting projectors on hyperplanes whose existence was established by H. Busemann. If m=2, density contractors
Externí odkaz:
http://arxiv.org/abs/1812.04520
Autor:
De Pauw, Thierry, Züst, Roger
Publikováno v:
American Journal of Mathematics, Volume 141, Number 6, 2019, pp. 1591-1705
We adapt to an infinite dimensional ambient space E.R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$
Externí odkaz:
http://arxiv.org/abs/1602.06941
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