Torsional rigidity of submanifolds with controlled geometry
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Torsional rigidity of submanifolds with controlled geometryDate
2009Publisher
Springer VerlagISSN
0025-5831Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
We prove explicit upper and lower bounds for the torsional
rigidity of extrinsic domains of submanifolds Pm with controlled radial
mean curvature in ambient Riemannian manifolds Nn with a pole p and
with sectional ... [+]
We prove explicit upper and lower bounds for the torsional
rigidity of extrinsic domains of submanifolds Pm with controlled radial
mean curvature in ambient Riemannian manifolds Nn with a pole p and
with sectional curvatures bounded from above and from below, respec-
tively. These bounds are given in terms of the torsional rigidities of
corresponding Schwarz symmetrizations of the domains in warped prod-
uct model spaces. Our main results are obtained using methods from
previously established isoperimetric inequalities, as found in e.g. [MP4]
and [MP5]. As in [MP4] we also characterize the geometry of those situ-
ations in which the bounds for the torsional rigidity are actually attained
and study the behavior at in¯nity of the so-called geometric average of
the mean exit time for Brownian motion [-]
Is part of
Mathematische Annalen (0025-5831), vol. 344, no. 3 (2009), p. 511-542Rights
This item appears in the folowing collection(s)
- MAT_Articles [759]