133 research outputs found
Sharp constants in weighted trace inequalities on Riemannian manifolds
We establish some sharp weighted trace inequalities
W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M)
on dimensional compact smooth manifolds with smooth boundaries, where
is a defining function of and . This is stimulated
by some recent work on fractional (conformal) Laplacians and related problems
in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page
A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
We establish new existence and non-existence results for positive solutions
of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This
equation arises from the Hamiltonian constraint equation for the
Einstein-scalar field system in general relativity. Our analysis introduces
variational techniques, in the form of the mountain pass lemma, to the analysis
of the Hamiltonian constraint equation, which has been previously studied by
other methods.Comment: 15 page
Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary
Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with
smooth n-1 dimensional boundary. We search the positive solutions of the
singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann
boundary conditions or for the singularly perturbed Klein Gordon Maxwell system
with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that
stable critical points of the mean curvature of the boundary generates
solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884
A compactness theorem for scalar-flat metrics on manifolds with boundary
Let (M,g) be a compact Riemannian manifold with boundary. This paper is
concerned with the set of scalar-flat metrics which are in the conformal class
of g and have the boundary as a constant mean curvature hypersurface. We prove
that this set is compact for dimensions greater than or equal to 7 under the
generic condition that the trace-free 2nd fundamental form of the boundary is
nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential
Equation
Existence of solutions to a higher dimensional mean-field equation on manifolds
For we prove an existence result for the equation on a closed Riemannian
manifold of dimension for certain values of .Comment: 15 Page
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces
We consider a singular Liouville equation on a compact surface, arising from
the study of Chern-Simons vortices in a self dual regime. Using new improved
versions of the Moser-Trudinger inequalities (whose main feature is to be
scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF
Asymptotic behavior of solutions to the -Yamabe equation near isolated singularities
-Yamabe equations are conformally invariant equations generalizing
the classical Yamabe equation. In an earlier work YanYan Li proved that an
admissible solution with an isolated singularity at to the
-Yamabe equation is asymptotically radially symmetric. In this work
we prove that an admissible solution with an isolated singularity at to the -Yamabe equation is asymptotic to a radial
solution to the same equation on . These results
generalize earlier pioneering work in this direction on the classical Yamabe
equation by Caffarelli, Gidas, and Spruck. In extending the work of Caffarelli
et al, we formulate and prove a general asymptotic approximation result for
solutions to certain ODEs which include the case for scalar curvature and
curvature cases. An alternative proof is also provided using
analysis of the linearized operators at the radial solutions, along the lines
of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen.Comment: 55 page
A phasing and imputation method for pedigreed populations that results in a single-stage genomic evaluation
<p>Abstract</p> <p>Background</p> <p>Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation.</p> <p>Methods</p> <p>An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis.</p> <p>Results</p> <p>Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored.</p> <p>Conclusions</p> <p>The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.</p
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