Search results for "Geometry and Topology"

Numerical bounds for semi-stable families of curves or of certain higher-dimensional manifolds

2005

Given an open subset U U of a projective curve Y Y and a smooth family f : V → U f:V\to U of curves, with semi-stable reduction over Y Y , we show that for a subvariation V \mathbb {V} of Hodge structures of R 1 f ∗ C V R^1f_*\mathbb {C}_V with rank ( V ) > 2 \textrm {rank} (\mathbb {V})>2 the Arakelov inequality must be strict. For families of n n -folds we prove a similar result under the assumption that the ( n , 0 ) (n,0) component of the Higgs bundle of V \mathbb {V} defines a birational map.

Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2

1996

Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.

Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

2019

The index of stable critical points

2002

Abstract In this paper we show that in dimension greater or equal than 3 the index of a stable critical point can be any integer. More concretely, given any k∈ Z and n⩾3 we construct a C ∞ vector field on R n with a unique critical point which is stable (in positive and negative time) and has index equal to k. This result extends previous ones on the index of stable critical points.

A comparison theorem for the mean exit time from a domain in a K�hler manifold

1992

Let M be a Kahler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. Let ω be a domain in M with some bounds on the mean and JN-mean curvatures of its boundary ∂ω. The main result of this paper is a comparison theorem between the Mean Exit Time function defined on ω and the Mean Exit Time from a geodesic ball of the complex projective space ℂℙ n (λ) which involves a characterization of the geodesic balls among the domain ω. In order to achieve this, we prove a comparison theorem for the mean curvatures of hypersurfaces parallel to the boundary of ω, using the Index Lemma for Submanifolds.

Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction

2020

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.

On the ultradistributions of Beurling type

2009

Sea un conjunto abierto no vac´ýo del espacio euclideo . En este articulo se demuestra que si S es una ultradistribucion en , perteneciente a una clase de tipo Beurling que sea estable frente a operadores diferenciales, entonces S se puede representar en la formaP2Nk0 Df, donde f es una funcion compleja definida en que es Lebesgue medible y esencialmente acotada en cada subconjunto compacto de . Tambi´en se obtienen otros resultados de estructura de ciertas ultradistribuciones.

Special issue on geometric constraints and reasoning

2012

Maximal subgroups of small index of finite almost simple groups

2022

We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\operatorname{l}(S)^2}$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by $\log^3 {\operatorname{l}(S)}$ and $\operatorname{l}(S)^2 < |S|$.

On the structure of certain ultradistributions

2009

Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f, 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.