Riesz $s$-equilibrium measures on $d$-rectifiable sets as $s$ approaches $d$
| dc.creator | Calef, M. T. | |
| dc.creator | Hardin, D. P. | |
| dc.date | 2008-08-28 | |
| dc.date.accessioned | 2026-07-07T09:59:01Z | |
| dc.date.available | 2026-07-07T09:59:01Z | |
| dc.description | Let $A$ be a compact set in ${\mathbb R}^p$ of Hausdorff dimension $d$. For $s\in(0,d)$, the Riesz $s$-equilibrium measure $μ^s$ is the unique Borel probability measure with support in $A$ that minimizes $$ I_s(μ):=\iint\frac{1}{|x-y|^s}dμ(y)dμ(x)$$ over all such probability measures. If $A$ is strongly $({\mathcal H}^d, d)$-rectifiable, then $μ^s$ converges in the weak-star topology to normalized $d$-dimensional Hausdorff measure restricted to $A$ as $s$ approaches $d$ from below. | |
| dc.identifier | https://arxiv.org/abs/0808.3802 | |
| dc.identifier | http://arxiv.org/abs/0808.3802 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167885 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 31C15 | |
| dc.title | Riesz $s$-equilibrium measures on $d$-rectifiable sets as $s$ approaches $d$ | |
| dc.type | text |