G. Pacelli Bessa
Riemannian submersions with discrete spectrum.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: G. Pacelli Bessa, J. Fabio Montenegro, Paolo Piccione
Subjects: Differential Geometry
AbstractWe prove some estimates on the spectrum of the Laplacian of the total space
of a Riemannian submersion in terms of the spectrum of the Laplacian of the
base and the geometry of the fibers. When the fibers of the submersions are
compact and minimal, we prove that the total space is discrete if and only if
the base is discrete. When the fibers are not minimal, we prove a discreteness
criterion for the total space in terms of the relative growth of the mean
curvature of the fibers and the mean curvature of the geodesic spheres in the
base.An estimate for the sectional curvature of cylindrically bounded submanifolds.
Mon, 11/23/2009 - 16:01 — SomNambulAuthors: Luis J. Alias, G. Pacelli Bessa, J. Fabio Montenegro
Subjects: Differential Geometry
AbstractWe give sharp sectional curvature estimates for complete immersed
cylindrically bounded $m$-submanifolds $\varphi:M\to N\times\mathbb{R}^{\ell}$,
$n+\ell\leq 2m-1$ provided that either $\varphi$ is proper with the second
fundamental form with certain controlled growth or $M$ has scalar curvature
with strong quadratic decay. This latter gives a non-trivial extension of the
Jorge-Koutrofiotis Theorem [7]Stochastic completeness and volume growth.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Christian Baer, G. Pacelli Bessa
Subjects: Differential Geometry
AbstractIt has been suggested in 1999 that a certain volume growth condition for
geodesically complete Riemannian manifolds might imply that the manifold is
stochastically complete. This is motivated by a large class of examples and by
a known analogous criterion for recurrence of Brownian motion. We show that the
suggested implication is not true in general. We also give counter-examples to
a converse implication.
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