322 research outputs found
Asymptotic analysis for fourth order Paneitz equations with critical growth
We investigate fourth order Paneitz equations of critical growth in the case
of -dimensional closed conformally flat manifolds, . Such equations
arise from conformal geometry and are modelized on the Einstein case of the
geometric equation describing the effects of conformal changes of metrics on
the -curvature. We obtain sharp asymptotics for arbitrary bounded energy
sequences of solutions of our equations from which we derive stability and
compactness properties. In doing so we establish the criticality of the
geometric equation with respect to the trace of its second order terms.Comment: 35 pages. To appear in "Advances in the Calculus of Variations
Sharp Nash inequalities on manifolds with boundary in the presence of symmetries
In this paper we establish the best constant
for the Trace Nash inequality on a dimensional compact Riemannian manifold
in the presence of symmetries, which is an improvement over the classical case
due to the symmetries which arise and reflect the geometry of manifold. This is
particularly true when the data of the problem is invariant under the action of
an arbitrary compact subgroup of the isometry group , where all
the orbits have infinite cardinal
Remarks on the extension of the Ricci flow
We present two new conditions to extend the Ricci flow on a compact manifold
over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi
Rigidity of noncompact complete Bach-flat manifolds
Let be a noncompact complete Bach-flat manifold with positive Yamabe
constant. We prove that is flat if has zero scalar curvature
and sufficiently small bound of curvature tensor. When has
nonconstant scalar curvature, we prove that is conformal to the flat
space if has sufficiently small bound of curvature tensor and
bound of scalar curvature.Comment: 10 pages, To appear J. Geom. Physic
Function Spaces on Singular Manifolds
It is shown that most of the well-known basic results for Sobolev-Slobodeckii
and Bessel potential spaces, known to hold on bounded smooth domains in
, continue to be valid on a wide class of Riemannian manifolds
with singularities and boundary, provided suitable weights, which reflect the
nature of the singularities, are introduced. These results are of importance
for the study of partial differential equations on piece-wise smooth domains.Comment: 37 pages, 1 figure, final version, augmented by additional
references; to appear in Math. Nachrichte
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