Toward Best Isoperimetric Constants for $(H^1,BMO)$-Normal Conformal Metrics on $\mathbb R^n$, $n\ge 3$
| dc.creator | Xiao, Jie | |
| dc.date | 2008-01-30 | |
| dc.date | 2008-08-12 | |
| dc.date.accessioned | 2026-07-07T09:55:47Z | |
| dc.date.available | 2026-07-07T09:55:47Z | |
| dc.description | The aim of this article is: (a) To establish the existence of the best isoperimetric constants for the $(H^1,BMO)$-normal conformal metrics $e^{2u}|dx|^2$ on $\mathbb R^n$, $n\ge 3$, i.e., the conformal metrics with the Q-curvature orientated conditions $$ (-Δ)^{n/2}u\in H^1(\mathbb R^n) & \ u(x)=\hbox{const.}+\frac{\int_{\mathbb R^n}(\log\frac{|\cdot|}{|x-\cdot|})(-Δ)^{n/2} u(\cdot) d\mathcal{H}^n(\cdot)}{2^{n-1}π^{n/2}Γ(n/2)}; $$ (b) To prove that $(nω_n^\frac1n)^\frac{n}{n-1}$ is the optimal upper bound of the best isoperimetric constants for the complete $(H^1,BMO)$-normal conformal metrics with nonnegative scalar curvature; (c) To find the optimal upper bound of the best isoperimetric constants via the quotients of two power integrals of Green's functions for the $n$-Laplacian operators $-\hbox{div}(|\nabla u|^{n-2}\nabla u)$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0801.4753 | |
| dc.identifier | http://arxiv.org/abs/0801.4753 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166752 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 53A30, 31B35 (Primary) 42B30 (Secondary) | |
| dc.title | Toward Best Isoperimetric Constants for $(H^1,BMO)$-Normal Conformal Metrics on $\mathbb R^n$, $n\ge 3$ | |
| dc.type | text |