Torsional rigidity of submanifolds with controlled geometry
Torsional rigidity of submanifolds with controlled geometry
复制标题
具有受控几何形状的子歧管的扭转刚度
DOI：
10.1007/s00208-008-0315-3
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
V. Palmer
中科院分区：
文献类型：
--
作者：
A. Hurtado;S. Markvorsen;V. Palmer
我们证明了明确的上和下界的外部域的submanifoldsPm的扭转刚度与控制的径向平均曲率在周围的黎曼流形Nn与极点的截面曲率有界从上方和从下方，分别。这些界限给出了相应的施瓦茨对称化的域在翘曲的产品模型空间的扭转刚度。我们的主要结果是使用以前建立的等周不等式的方法得到的，例如，Markvorsen和Palmer（Proc Lond Math Soc 93：253- 272，2006; Extrinsic isoperimetric analysis on submanifold with curvatures bounded from below，p.39，preprint，2007）.正如在那篇论文中，我们还描述了这些情况下的几何，其中的扭转刚度的界限实际上是达到和研究的行为在无穷大的所谓的几何平均的平均退出时间的布朗运动。
We prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifoldsPmwith controlled radial mean curvature in ambient Riemannian manifoldsNnwith a polepand with sectional curvatures bounded from above and from below, respectively. These bounds are given in terms of the torsional rigidities of corresponding Schwarz-symmetrization of the domains in warped product model spaces. Our main results are obtained using methods from previously established isoperimetric inequalities, as found in, e.g., Markvorsen and Palmer (Proc Lond Math Soc 93:253--272, 2006; Extrinsic isoperimetric analysis on submanifolds with curvatures bounded from below, p. 39, preprint, 2007). As in that paper we also characterize the geometry of those situations in which the bounds for the torsional rigidity are actually attained and study the behavior at infinity of the so-calledgeometric averageof the mean exit time for Brownian motion.