3,580 research outputs found
Curvature Estimates for Critical 4-Manifolds with a Lower Ricci Curvature Bound
We draw elliptic regularity results for 4-manifolds with an elliptic system,
without Sobolev constant control. Direct use of analysis is circumvented; the
results come mainly through geometric and topological arguments. In contrast to
our previous paper, which worked predominantly on the scale of the curvature
radius, the results here provide curvature controls on a fixed scale
Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing Field
Given a complete, Ricci-flat 4-manifold with a Killing field, we give an
estimate on the manifold's energy in terms of a certain asymptotic quantity of
the Killing field. If the Killing field has no zeros and satisfies a certain
asymptotic condition, the manifold is flat.Comment: Published Versio
Generalized Kahler Taub-NUTs and Two Exceptional Instantons
We study the one-parameter family of twisted Kahler Taub-NUT metrics
(discovered by Donaldson), along with two exceptional Taub-NUT-like instantons,
and understand them to the extend that should be sufficient for blow-up and
gluing arguments. In particular we parametrize their geodesics from the origin,
determine curvature fall-off rates, volume growth rates for metric balls, and
find blow-down limits
Topology of K\"ahler manifolds with weakly pseudoconvex boundary
We study Kahler manifolds-with-boundary, not necessarily compact, with weakly
pseudoconvex boundary, each component of which is compact. If such a manifold
has boundary components (possibly ), then it has first
betti number at least , and the Levi form of any boundary component is
zero. If has pseudoconvex boundary components and at least one
non-parabolic end, the first betti number of is at least . In either
case, any boundary component has non-vanishing first betti number. If has
one pseudoconvex boundary component with vanishing first betti number, the
first betti number of is also zero. Especially significant are applications
to Kahler ALE manifolds, and to Kahler 4-manifolds. This significantly extends
prior results in this direction (eg. Kohn-Rossi), and uses substantially
simpler methods.Comment: Published Versio
Classification of polytope metrics and complete scalar-flat K\"ahler 4-Manifolds with two symmetries
We study unbounded 2-dimensional metric polytopes such as those arising as
K\"ahler quotients of complete K\"ahler 4-manifolds with two commuting
symmetries and zero scalar curvature. Under a mild closedness condition, we
obtain a complete classification of metrics on such polytopes, and as a result
classify all possible metrics on on the corresponding K\"ahler 4-manifolds. If
the polytope is the plane or half-plane then only flat metrics are possible,
and if the polytope has one corner then the 2-parameter family of generalized
Taub-NUTs (discovered by Donaldson) are indeed the only possible metrics.
Polytopes with edges admit an -dimensional family of possible
metrics.Comment: 54 pages, 22 figure
Convergence of compact Ricci solitons
We show that sequences of compact gradient Ricci solitons converge to
complete orbifold gradient solitons, assuming constraints on volume, the
-norm of curvature, and the auxiliary constant . The strongest
results are in dimension 4, where curvature bounds are equivalent to
upper bounds on the Euler number. We obtain necessary and sufficient conditions
for limits to be compact
Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature Bound
We study critical Riemannian 4-manifolds with a lower bound on Ricci
curvature, but no a priori analytic constraints such as on Sobolev constants.
We derive elliptic-type estimates for the local curvature radius, which itself
controls sectional curvature. The primary method is construction of blow-ups of
degenerating metrics, followed by a geometric/topological triviality result
from a previous work.Comment: The third uploaded version corrects some potentially confusing
typographical errors. No material adjustments were mad
Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds
We consider the moduli space of the extremal K\"ahler metrics on compact
manifolds. We show that under the conditions of two-sided total volume bounds,
-norm bounds on \Riem, and Sobolev constant bounds, this Moduli
space can be compactified by including (reduced) orbifolds with finitely many
singularities. Most of our results go through for certain other classes of
critical Riemannian metrics.Comment: 72 page
On Conformally Kaehler, Einstein Manifolds
We prove that any compact complex surface with positive first Chern class
admits an Einstein metric which is conformally related to a Kaehler metric. The
key new ingredient is the existence of such a metric on the blow-up of the
complex projective plane at two distinct points.Comment: 45 pages, 9 figures. Simplified proof of Lemma 25. Several minor
corrections to section
Spectrogram Feature Losses for Music Source Separation
In this paper we study deep learning-based music source separation, and
explore using an alternative loss to the standard spectrogram pixel-level L2
loss for model training. Our main contribution is in demonstrating that adding
a high-level feature loss term, extracted from the spectrograms using a VGG
net, can improve separation quality vis-a-vis a pure pixel-level loss. We show
this improvement in the context of the MMDenseNet, a State-of-the-Art deep
learning model for this task, for the extraction of drums and vocal sounds from
songs in the musdb18 database, covering a broad range of western music genres.
We believe that this finding can be generalized and applied to broader machine
learning-based systems in the audio domain.Comment: Accepted for presentation at the 27th European Signal Processing
Conference (EUSIPCO 2019
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