Search results for " mani"

Arithmeticity of Four Hypergeometric Monodromy Groups Associated to Calabi–Yau Threefolds: Table 1.

2014

In [12], we show that three of the fourteen hypergeometric monodromy groups associated to Calabi-Yau threefolds are arithmetic. Brav-Thomas (in [3]) show that seven of the remaining eleven are thin. In this article, we settle the arithmeticity problem for the fourteen monodromy groups, by showing that, the remaining four are arithmetic.

Frobenius polynomials for Calabi–Yau equations

2008

We describe a variation of Dwork’ s unit-root method to determine the degree 4 Frobenius polynomial for members of a 1-modulus Calabi–Yau family over P1 in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples from the list [3]. For singular points, we find that the Frobenius polynomial splits in a product of two linear factors and a quadratic part 1− apT + p3T 2. We identify weight 4 modular forms which reproduce the ap as Fourier coefficients.

Bounds for the first Dirichlet eigenvalue attained at an infinite family of Riemannian manifolds

1996

LetM be a compact Riemannian manifold with smooth boundary ∂M. We get bounds for the first eigenvalue of the Dirichlet eigenvalue problem onM in terms of bounds of the sectional curvature ofM and the normal curvatures of ∂M. We discuss the equality, which is attained precisely on certain model spaces defined by J. H. Eschenburg. We also get analog results for Kahler manifolds. We show how the same technique gives comparison theorems for the quotient volume(P)/volume(M),M being a compact Riemannian or Kahler manifold andP being a compact real hypersurface ofM.

Connexion markovienne, courbure et formule de Weitzenböck sur l'espace des chemins riemanniens

2001

Resume Nous considerons la connexion markovienne sur l'espace des chemins riemanniens. Le tenseur de courbure est calcule explicitement et une formula de Weitzenbock est etablie.

The Poisson embedding approach to the Calderón problem

2020

We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.

Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents

1984

Abstract In this paper we study the existence of nontrivial solutions for the boundary value problem { − Δ u − λ u − u | u | 2 ⁎ − 2 = 0 in Ω u = 0 on ∂ Ω when Ω⊂Rn is a bounded domain, n ⩾ 3, 2 ⁎ = 2 n ( n − 2 ) is the critical exponent for the Sobolev embedding H 0 1 ( Ω ) ⊂ L p ( Ω ) , λ is a real parameter. We prove that there is bifurcation from any eigenvalue λj of − Δ and we give an estimate of the left neighbourhoods ] λ j ⁎ , λj] of λj, j∈N, in which the bifurcation branch can be extended. Moreover we prove that, if λ ∈ ] λ j ⁎ , λj[, the number of nontrivial solutions is at least twice the multiplicity of λj. The same kind of results holds also when Ω is a compact Riemannian manif…

Connected sums and the infimum of the Yamabe functional

1986

The classification of 4-dimensional homogeneous D'Atri spaces revisited

2007

Abstract In this short note we correct the (incomplete) classification theorem from [F. Podesta, A. Spiro, Four-dimensional Einstein-like manifolds and curvature homogeneity, Geom. Dedicata 54 (1995) 225–243], we improve a result from [P. Bueken, L. Vanhecke, Three- and four-dimensional Einstein-like manifolds and homogeneity, Geom. Dedicata 75 (1999) 123–136] and we announce the final solution of the classification problem for 4-dimensional homogeneous D'Atri spaces.

Quantum moment maps and invariants for G-invariant star products

2002

We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star products.

Closed star products and cyclic cohomology

1992

We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy t…