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C k -estimates for the ∂ ¯ -equation on concave domains of finite type

William Alexandre (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

C k estimates for convex domains of finite type in ℂ n are known from [7] for k = 0 and from [2] for k > 0 . We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching z and ζ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work. To overcome this problem...

C*-actions.

Andrew John Sommese, James B. Carrell (1978)

Mathematica Scandinavica

Calabi flow on toric varieties with bounded Sobolev constant, I

Hongnian Huang (2016)

Complex Manifolds

Let (X, P) be a toric variety. In this note, we show that the C0-norm of the Calabi flow φ(t) on X is uniformly bounded in [0, T) if the Sobolev constant of φ(t) is uniformly bounded in [0, T). We also show that if (X, P) is uniform K-stable, then the modified Calabi flow converges exponentially fast to an extremal Kähler metric if the Ricci curvature and the Sobolev constant are uniformly bounded. At last, we discuss an extension of our results to a quasi-proper Kähler manifold.

Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II

Takashi Aoki (1986)

Annales de l'institut Fourier

Soit P un opérateur pseudodifférentiel (ou microdifférentiel) tel que exp P soit aussi un opérateur pseudodifférentiel. Alors le symbole de exp P s’ecrit exp q avec un symbole q . Pour la réciproque, si Q est un opérateur à symbole exp q , il existe un opérateur P tel que Q = exp P . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.

Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I

Takashi Aoki (1983)

Annales de l'institut Fourier

Cet article s’intéresse au calcul symbolique des opérateurs microdifférentiels avec symboles exponentiels. On donne la loi de composition des symboles exponentiels. Comme application, on trouve une condition suffisante d’ellipticité pour les opérateurs microdifférentiels d’ordre infini.

Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces

Klaus Hulek, Remke Kloosterman (2011)

Annales de l’institut Fourier

In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4 -space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.

Canonical contact forms on spherical CR manifolds

Wei Wang (2003)

Journal of the European Mathematical Society

We construct the CR invariant canonical contact form can ( J ) on scalar positive spherical CR manifold ( M , J ) , which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold Ω ( Γ ) / Γ , where Γ is a convex cocompact subgroup of Aut C R S 2 n + 1 = P U ( n + 1 , 1 ) and Ω ( Γ ) is the discontinuity domain of Γ . This contact form can be used to prove that Ω ( Γ ) / Γ is scalar positive (respectively, scalar negative, or scalar vanishing) if and...

Canonical metrics on some domains of ℂ n

Fabio Zuddas (2008/2009)

Séminaire de théorie spectrale et géométrie

The study of the existence and uniqueness of a preferred Kähler metric on a given complex manifold M is a very important area of research. In this talk we recall the main results and open questions for the most important canonical metrics (Einstein, constant scalar curvature, extremal, Kähler-Ricci solitons) in the compact and the non-compact case, then we consider a particular class of complex domains D in ℂ n , the so-called Hartogs domains, which can be equipped with a natural Kaehler metric g ....

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