Subanalytic version of Whitney's extension theorem
For any subanalytic -Whitney field (k finite), we construct its subanalytic -extension to . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.
Subelliptic estimates
Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications
The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.
Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.
Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
Let be a pseudoconvex domain in and let be a plurisubharmonic function in . For each we consider the -dimensional slice of , , let be the restriction of to and denote by the Bergman kernel of with the weight function . Generalizing a recent result of Maitani and Yamaguchi (corresponding to and ) we prove that is a plurisubharmonic function in . We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in the setting...
Submanifolds in the variety of planar normal sections.
Submanifolds of PN with Splitting Normal Bundle Sequence are Linear.
Submersions and equivariant Quillen metrics
In this paper, we calculate the behaviour of the equivariant Quillen metric by submersions. We thus extend a formula of Berthomieu-Bismut to the equivariant case.
Subordination Chains and Univalence of Holomorphic Mappings in Cn.
Subordination theory for holomorphic mappings of several complex variables
The authors obtain a generalization of Jack-Miller-Mocanu’s lemma and, using the technique of subordinations, deduce some properties of holomorphic mappings from the unit polydisc in into .
Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity
Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...
Subsets of Hardy-class zero sets in the ball.
We consider the problem of whether the union of complex hyperplanes can be a subset of a zero variety for the Hardy classes of the ball. A sufficient condition is found, consisting in a strong geometric separatedness requirement, together with a quantitative requirement slightly stronger than the necessary condition for Nevanlinna class zero varieties.
Subvarieties of parallelizable manifolds.
Successioni crescenti di -coppie di runge di varietà analitiche complesse
Sufficient conditions for univalence in .
Sui fibrati analitici reali -principali. II. - Teoremi di classificazione
Sui lemmi di preparazione per gli anelli di serie ristrette
Sul problema pluriarmonico in un campo sferico di per
Let be the boundary of the unit ball of . A set of second order linear partial differential operators, tangential to , is explicitly given in such a way that, for , the corresponding PDE caractherize the trace of the solution of the pluriharmonic problem (either “in the large” or “local”), relative to .
Sul teorema di Cauchy-Morera per le funzioni analitiche di più variabili complesse
A Cauchy-Morera theorem is proved for a function of complex variables, assuming only . A related result of Bochner, concerning continuous functions, is extended to a larger function class.