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On the real secondary classes of transversely holomorphic foliations

Taro Asuke (2000)

Annales de l'institut Fourier

In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space $H^{*} ({WO}_{2 q})$ of the real secondary classes to the space $H^{*} ({WU}_{q})$ of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...

On the Real Spectrum of a Ring of Global Analytic Functions

Jesùs M. Ruiz (1986)

Publications mathématiques et informatique de Rennes

On the reducibility of connections on the prolongations of vector bundles

Ivan Kolář (1974)

Colloquium Mathematicae

On the regularity of solutions in Convex Integration theory.

David Spring (1991)

Inventiones mathematicae

On the relation between elliptic and parabolic Harnack inequalities

Waldemar Hebisch, Laurent Saloff-Coste (2001)

Annales de l’institut Fourier

We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for $Δ$ on $M$ , (i.e., for $\partial_{t} + Δ$ ) and elliptic Harnack inequality for $- \partial_{t}^{2} + Δ$ on $ℝ \times M$ .

On the relation between the Einstein and the Komar expressions for the energy of the gravitational field

Piotr Tadeusz Chruściel (1985)

Annales de l'I.H.P. Physique théorique

On the relative Nash approximation of analytic maps.

Alberto Tancredi, Alberto Tognoli (1998)

Revista Matemática Complutense

On the renormalization group iteration of a two-dimensional hierarchical non-linear $O (N) σ$ -model

A. Pordt, T. Reisz (1991)

Annales de l'I.H.P. Physique théorique

On the Resolution of Degenerate Closed Geodescis.

Carlos J. Ferraris (1980)

Mathematische Zeitschrift

On the rho invariant for manifolds with boundary.

Kirk, Paul, Lesch, Matthias (2003)

Algebraic & Geometric Topology

On the rigidity of horizontal slices.

Lu, Zhiqin (2002)

Portugaliae Mathematica. Nova Série

On the Schrödinger heat kernel in horn-shaped domains

Gabriele Grillo (2004)

Colloquium Mathematicae

We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.

On the second order absolute differentiation

Cabras, Antonella, Kolář, Ivan (1999)

Proceedings of the 18th Winter School "Geometry and Physics"

In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)] I. Kolar,...

On the simplicial structure of some Weil bundles

Kureš, Miroslav (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

The author considers the problem to give explicit descriptions for several types of bundles on smooth manifolds, naturally related with the bundle of $k$ -dimensional velocities, or $k$ -jets. In fact, this kind of bundles are very natural objects in differential geometry, mechanics and Lagrangian dynamics. For this the author considers Weil bundles that arose from Weil algebras. If a suitable combinatorial data is provided by a simplicial coloured structure, then the author describes the corresponding...

On the singular set of stationary harmonic maps.

Fabrice Bethuel (1993)

Manuscripta mathematica

On the singularities of harmonic maps from a domain in $R^{3}$ into $S^{2}$

J. M. Coron (1986/1987)

Séminaire Équations aux dérivées partielles (Polytechnique)

On the Size of Balls Covered by Analytic Transformations.

Lawrence A. Harris (1977)

Monatshefte für Mathematik

On the size of the sets of gradients of bump functions and starlike bodies on the Hilbert space

Daniel Azagra, Mar Jiménez-Sevilla (2002)

Bulletin de la Société Mathématique de France

We study the size of the sets of gradients of bump functions on the Hilbert space $ℓ_{2}$ , and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in $ℓ_{2}$ can be. We find that those sets can be quite small. On the one hand, the usual norm of the Hilbert space $ℓ_{2}$ can be uniformly approximated by $C^{1}$ smooth Lipschitz functions $ψ$ so that the cones generated by the ranges of its derivatives $ψ^{'} (ℓ_{2})$ have empty interior. This implies that there are $C^{1}$ smooth Lipschitz bumps...

On the Sobolev constant and the $p$ -spectrum of a compact riemannian manifold

Peter Li (1980)

Annales scientifiques de l'École Normale Supérieure

On the space of asymptotically euclidean metrics

Lars Andersson (1989)

Compositio Mathematica

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