Search results for "Q2"
showing 10 items of 98 documents
SPANX-B and SPANX-C (Xq27 region) gene dosage analysis in Down’s syndrome subjects with undescended testes
2009
Down’s syndrome (DS) is one of the most common numer- ical chromosomal aberrations, usually caused by trisomy of chromosome 21, and is frequently complicated with congen- ital heart defects, duodenal obs truction and other conditions including undescended testis (UDT) (Fonkalsrud 1970). The incidence of undescended testes in DS was reported to be 6.52% (Chew and Hutson 2004) while the incidence of UDT in the first year is approximately 0.2%–0.8% in the nor- mal population (Benson et al . 1991; Ichiyanagi et al . 1998). Rapley et al . (2000) provided evidence for a testicular germ- cell tumours (TGCT) predisposition locus at Xq27; the au- thors obtained an hlod score of 4.7 from families wit…
Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions
2023
In a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, we prove sharp growth and integrability results for $p$-harmonic Green functions and their minimal $p$-weak upper gradients. We show that these properties are determined by the growth of the underlying measure near the singularity. Corresponding results are obtained also for more general $p$-harmonic functions with poles, as well as for singular solutions of elliptic differential equations in divergence form on weighted $\mathbf{R}^n$ and on manifolds. The proofs are based on a new general capacity estimate for annuli, which implies precise pointwise estimates for $p$-harmonic Green functions…
Semianalyticity of isoperimetric profiles
2009
It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
Failure of the local-to-global property for CD(K,N) spaces
2016
Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitable non convex subset of R^2 equipped with the l^\infty-norm and the Lebesgue measure. Combining many such spaces gives a (non compact) complete geodesic metric measure space satisfying CD(0,4) locally but failing CD(K,N) globally for every K and N.
Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds
2012
Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).
On the shape of compact hypersurfaces with almost constant mean curvature
2015
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
2014
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter to prove suitable generalizations of Brenier's theorem of existence of optimal maps.
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
2011
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\'e inequality is implied by the weak displacement convexity of the functional.
Failure of topological rigidity results for the measure contraction property
2014
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.
Dimensional reduction for energies with linear growth involving the bending moment
2008
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.