论文标题
最小化船体，P容量和等等不等式的完全riemannian歧管
Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
论文作者
论文摘要
严格向外最小化船体的概念已被研究，以坐在完全非策略的riemannian歧管内的一组有限周围。在环境流形的自然几何假设下，严格的向外最小化hull $ω^*$的$ω$的hull $ω^*$的特征是障碍物最小面积问题的最大体积解决方案，其中障碍物本身就是障碍物本身。如果$ω$具有$ \ mathscr {c}^{1，α} $ - 边界，则将$ \ partialω^*$的面积作为$ p $ - $ω$的限制恢复为$ p $ω$的限制，为$ p \ to $ p \ to 1^+$。最后，基于严格的外向疲劳的建立，在完全的非政策歧管上推断出具有非负RICCI曲率的尖锐等级不平等，提供了$ 3 \ leq n \ leq 7 $。
The notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric assumptions on the ambient manifold, the strictly outward minimising hull $Ω^*$ of a set $Ω$ is characterised as a maximal volume solution of the least area problem with obstacle, where the obstacle is the set itself. In the case where $Ω$ has $\mathscr{C}^{1, α}$-boundary, the area of $\partial Ω^*$ is recovered as the limit of the $p$-capacities of $Ω$, as $p \to 1^+$. Finally, building on the existence of strictly outward minimising exhaustions, a sharp isoperimetric inequality is deduced on complete noncompact manifolds with nonnegative Ricci curvature, provided $3 \leq n \leq 7$.
