We study the problem of existence regions separating a given amount volume with least possible perimeter inside Euclidean cone. Our main result shows that nonexistence for implies isoperimetric profile cone coincides one half-space. This allows us to give some criteria ensuring regions: instance, local convexity at boundary point. also characterize which are stable in convex cone, i.e., second order minima under constraint. From this it follows euclidean balls centered vertex intersected

We prove that the isoperimetric profile of a convex domain Ω with compact closure in Riemannian manifold (M n+1 , g) satisfies second-order differential inequality only depends on dimension and lower bound Ricci curvature Q. Regularity properties topological consequences regions arise naturally from this point view. Moreover, by integrating inequality, we obtain sharp comparison theorems: not can derive an should be compared Levy-Gromov Inequality but also show if Ric > n6 Q, then Q is...

We use variational arguments to introduce a notion of mean curvature for surfaces in the Heisenberg group H^1 endowed with its Carnot-Carathéodory distance. By analyzing first variation area, we characterize C^2 stationary area as those zero (or constant if volume-preserving condition is assumed) and such that characteristic curves meet orthogonally singular curves. Moreover, Minkowski type formula relating curvature, volume obtained area-stationary enclosing given region. As consequence...

Antecedentes: La ansiedad y la depresión son síndromes psiquiátricos con gran prevalencia en el mundo (5-50%)que por lo general se presentan juntos generan a sociedad una importante carga social económica. Losalumnos universitarios, especialmente los que tienen alta académica como estudiantes de medicina, sonvulnerables estos trastornos. Objetivos: Determinar sintomatología ansiosa depresiva alumnosde medicina relacionarla variables edad, sexo año estudios. Material Métodos: Se evaluó...

In this paper we study sets in the $n$-dimensional Heisenberg group $\hhn$ which are critical points, under a volume constraint, of sub-Riemannian perimeter associated to distribution horizontal vector fields $\hhn$. We define notion mean curvature for hypersurfaces and show that boundary stationary set is constant (CMC) hypersurface. Our definition coincides with previous ones. main result describes CMC revolution The fact such hypersurface invariant compact rotations allows us reduce...

Abstract Let be an open half-space or slab in ℝ n+1 endowed with a perturbation of the Gaussian measureof form f (p) := exp(ω(p) − c|p| 2 ), where c > 0 and ω is smooth concave function depending only onthe signed distance from linear hyperplane parallel to ∂ Ω. In this work we follow variational approach show that half-spaces perpendicular Ω uniquely minimize weighted perimeter among sets enclosing same volume. The main ingredient proof characterization half-spacesparallel as unique...

We consider the isoperimetric problem of minimizing perimeter for given volume in a strictly convex domain Q c R n+1 and prove that, if is rotationally symmetric about some line, then any solution to this must be convex.

In the present paper we show data obtained from a normal population with racially mixed profile typical of city São Paulo, State Paulo. Data were generated polymerase chain reaction using sequence specific primers (PCR-SSP) for HLA-DRB and followed by hybridization oligonucleotide probes (PCR-SSO) HLA-DQA1 HLA-DQB1 loci. HLA-DRB, DQA1, DQB1 haplotype frequencies as well common linkage disequilibria found. This was also shown to be in genetic equilibrium according Hardy-Weinberg law. HLA-DR...

The great difficulties in treating people and animals suffering from cryptosporidiosis have prompted the development of vitro experimental models. Due to models culture, new extracellular stages Cryptosporidium been demonstrated. these phases depends on technique culture species genotype used. Here, we undertake molecular characterization by polymerase chain reaction-restriction fragment length polymorphism different isolates calves, concluding that all are C. parvum cattle genotype,...

We prove that the isoperimetric profile of a convex domain $Ω$ with compact closure in Riemannian manifold $(M^{n+1},g)$ satisfies second order differential inequality which only depends on dimension and lower bound Ricci curvature $Ω$. Regularity properties topological consequences regions arise naturally from this point view. Moreover, by integrating we obtain sharp comparison theorems: not can derive an should be compared Lévy-Gromov Inequality but also show if $\text{Ric}\geq nδ$ $Ω$,...

In a Riemannian manifold with smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of weighted perimeter under variations preserving volume. By assuming local convexity boundary and certain behavior Bakry–Émery–Ricci tensor deduce rigidity properties for sets by using deformations constructed from parallel vector fields tangent to boundary. As consequence, completely classify in some cylinders Ω×R product weights. Finally,...

We study the problem of existence regions separating a given amount volume with least possible perimeter inside Euclidean cone. Our main result shows that nonexistence for implies isoperimetric profile cone coincides one half-space. This allows us to give some criteria ensuring regions: instance, local convexity at boundary point. also characterize which are stable in convex cone, i.e., second order minima under constraint. From this it follows euclidean balls centered vertex intersected

A surface of constant mean curvature (CMC) equal to H in a sub-Riemannian 3-manifold is strongly stable if it minimizes the functional area+2Hvolume up second order. In this paper we obtain some criteria ensuring strong stability surfaces Sasakian 3-manifolds. We also produce new examples C1 complete CMC with empty singular set 3-space forms by studying those ones containing vertical line. As consequence, are able find non-vertical hyperbolic M(−1). relation Bernstein problem M(−1) discover...