100 research outputs found
Hurewicz fibrations, almost submetries and critical points of smooth maps
We prove that the existence of a Hurewicz fibration between certain spaces
with the homotopy type of a CW-complex implies some topological restrictions on
their universal coverings. This result is used to deduce differentiable and
metric properties of maps between compact Riemannian manifolds under curvature
restrictions
Some triviality results for quasi-Einstein manifolds and Einstein warped products
In this paper we prove a number of triviality results for Einstein warped
products and quasi-Einstein manifolds using different techniques and under
assumptions of various nature. In particular we obtain and exploit gradient
estimates for solutions of weighted Poisson-type equations and adaptations to
the weighted setting of some Liouville-type theorems.Comment: 15 pages, fixed minor mistakes in Section
Some non-linear function theoretic properties of Riemannian manifolds
We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the -Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators
A finiteness theorem for the space of Lp harmonic sections
In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of Lp harmonic sections of Riemannian or Hermitian vector bundles over complete manifolds. The geometric conditions on the manifold are subsumed by the assumption that the Morse index of a related Schro \u308dinger operator is finite. Applications of the finiteness theorem to concrete geometric situations are also presented
Reverse Khas'minskii condition
The aim of this paper is to present and discuss some equivalent
characterizations of p-parabolicity in terms of existence of special exhaustion
functions. In particular, Khas'minskii in [K] proved that if there exists a
2-superharmonic function k defined outside a compact set such that , then R is 2-parabolic, and Sario and Nakai in [SN] were
able to improve this result by showing that R is 2-parabolic if and only if
there exists an Evans potential, i.e. a 2-harmonic function with \lim_{x\to \infty} \E(x)=\infty. In this paper, we will prove a
reverse Khas'minskii condition valid for any p>1 and discuss the existence of
Evans potentials in the nonlinear case.Comment: final version of the article available at http://www.springer.co
The mean curvature of cylindrically bounded submanifolds
We give an estimate of the mean curvature of a complete submanifold lying
inside a closed cylinder in a product Riemannian manifold
. It follows that a complete hypersurface of given
constant mean curvature lying inside a closed circular cylinder in Euclidean
space cannot be proper if the circular base is of sufficiently small radius. In
particular, any possible counterexample to a conjecture of Calabion complete
minimal hypersurfaces cannot be proper. As another application of our method,
we derive a result about the stochastic incompleteness of submanifolds with
sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title
(February 2009). To appear in Mathematische Annale
The H\"older-Poincar\'e Duality for -cohomology
We prove the following version of Poincare duality for reduced
-cohomology: For any , the -cohomology of a
Riemannian manifold is in duality with the interior 1/p+1/p'=11/q+1/q'=1$.Comment: 21 page
Myers' type theorems and some related oscillation results
In this paper we study the behavior of solutions of a second order
differential equation. The existence of a zero and its localization allow us to
get some compactness results. In particular we obtain a Myers' type theorem
even in the presence of an amount of negative curvature. The technique we use
also applies to the study of spectral properties of Schroedinger operators on
complete manifolds.Comment: 16 page
Height estimates for Killing graphs
The paper aims at proving global height estimates for Killing graphs defined
over a complete manifold with nonempty boundary. To this end, we first point
out how the geometric analysis on a Killing graph is naturally related to a
weighted manifold structure, where the weight is defined in terms of the length
of the Killing vector field. According to this viewpoint, we introduce some
potential theory on weighted manifolds with boundary and we prove a weighted
volume estimate for intrinsic balls on the Killing graph. Finally, using these
tools, we provide the desired estimate for the weighted height in the
assumption that the Killing graph has constant weighted mean curvature and the
weighted geometry of the ambient space is suitably controlled.Comment: 26 pages. Final version. To appear on Journal of Geometric Analysi
Sequence similarity is more relevant than species specificity in probabilistic backtranslation
BACKGROUND: Backtranslation is the process of decoding a sequence of amino acids into the corresponding codons. All synthetic gene design systems include a backtranslation module. The degeneracy of the genetic code makes backtranslation potentially ambiguous since most amino acids are encoded by multiple codons. The common approach to overcome this difficulty is based on imitation of codon usage within the target species. RESULTS: This paper describes EasyBack, a new parameter-free, fully-automated software for backtranslation using Hidden Markov Models. EasyBack is not based on imitation of codon usage within the target species, but instead uses a sequence-similarity criterion. The model is trained with a set of proteins with known cDNA coding sequences, constructed from the input protein by querying the NCBI databases with BLAST. Unlike existing software, the proposed method allows the quality of prediction to be estimated. When tested on a group of proteins that show different degrees of sequence conservation, EasyBack outperforms other published methods in terms of precision. CONCLUSION: The prediction quality of a protein backtranslation methis markedly increased by replacing the criterion of most used codon in the same species with a Hidden Markov Model trained with a set of most similar sequences from all species. Moreover, the proposed method allows the quality of prediction to be estimated probabilistically
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