共查询到20条相似文献,搜索用时 265 毫秒
1.
William Alexandre 《Mathematische Zeitschrift》2006,252(3):473-496
For a bounded convex domain with C∞ smooth boundary of finite type m and q=1, . . . ,n−1, we construct a -solving integral operator T*q such that for all k ∈ ℕ and the usual Ck and -norms the operator is continuous. 相似文献
2.
William Alexandre 《Mathematische Zeitschrift》2006,253(2):263-280
Résumé Soient donnés D un domaine borné de , convexe, de type fini, X une hypersurface complexe telle que soit non vide, connexe et transverse et . Nous nous intéressons au problème suivant. Sous quelle(s) condition(s) existe-t-il telle que Φ|X = φ. Nous allons donner une condition nécessaire à l'existence de l'extension Φ puis sous une condition un peu plus forte nous
montrerons la continuité d'un opérateur d'extension de type Berndtsson-Andersson.
相似文献
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Let X be a weakly complete space i.e. X a complex space endowed with a Ck-smooth, k?0, plurisubharmonic exhaustion function. We give the notion of minimal kernelΣ1=Σ1(X) of X by the following property: x∈Σ1 if no continuous plurisubharmonic exhaustion function is strictly plurisubharmonic near x. The study of the geometric properties of the minimal kernels is the aim of present paper. After stating that the minimal kernel Σ1 of a weakly complete space can be defined by a single plurisubharmonic exhaustion function ?, called minimal, using the characterization in terms of Bremermann envelopes, we prove the following, crucial, result: if X is a weakly complete manifold and ? a minimal function for X, the nonempty level sets Σc1=Σ1∩{?=c} have the local maximum property. In the last section we discuss the special case of weakly complete surfaces. We prove that if dimcX=2 and c is a regular value of a minimal function ? then the nonempty level sets Σc1=Σ1∩{?=c} are compact spaces foliated by holomorphic curves. 相似文献
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Dejan Kolari? 《Differential Geometry and its Applications》2011,29(3):292-298
We prove the parametric homotopy principle for holomorphic immersions of Stein manifolds into Euclidean space and the homotopy principle with approximation on holomorphically convex sets. We write an integration by parts like formula for the solution f to the problem LfΣ|=g, where L is a holomorphic vector field, semi-transversal to analytic variety Σ. 相似文献
7.
Franc Forstnerič Björn Ivarsson Frank Kutzschebauch Jasna Prezelj 《Mathematische Annalen》2007,338(3):545-554
Given a Stein manifold x of dimension n > 1, a discrete sequence , and a discrete sequence where , there exists a proper holomorphic embedding satisfying f(a
j
) = b
j
for every j = 1,2,...
Forstnerič and Prezelj supported by grants P1-0291 and J1-6173, Republic of Slovenia.
Kutzschebauch supported by Schweizerische National fonds grant 200021-107477/1.
Ivarsson supported by The Wenner-Gren Foundations. 相似文献
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The Poincaré-Bertrand formula and the composition formula for the Bochner-Martinelli integral on piecewise smooth manifolds
are obtained. As an application, the regularization problem for linear singular integral equation with Bochner-Martinelli
kernel and variable coefficients is discussed. 相似文献
10.
Andrei Teleman 《Mathematische Annalen》2006,335(4):965-989
We describe the positive cone and the pseudo-effective cone of a non-Kählerian surface. We use these results for two types of applications: 1. Describe the set of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kählerian surface, and decide whether the assignment is a deformation invariant. 2. Study the stability of the canonical extension of a class VII surface X with positive b 2. This extension plays an important role in our strategy to prove existence of curves on class VII surfaces, using gauge theoretical methods [Te2]. Our main tools are Buchdahl ampleness criterion for non-Kählerian surfaces [Bu2] and the recent results of Dloussky-Oeljeklaus-Toma [DOT] and Dloussky [D] on class VII surfaces with curves. 相似文献
11.
We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domain which is a small deformation of a strictly linearly convex domain D⊂Cn with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for foliations by stationary disks through a given boundary point. 相似文献
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The aim of the present paper is to introduce a metric locally convex topology on the space
of δ-psh functions in the Cegrell class
. We prove that with this topology
is a non-separable and non-reflexive Fréchet space. At the same time, we extend the Monge–Ampère operator from the class
to
. 相似文献
14.
The E. Amar and G. Henkin theorem on the bounded extendability of bounded holomorphic functions from certain closed complex
submanifolds of strictly pseudoconvex domains to the whole domain is generalized to the case of finite type convex domains
and their intersections with affine linear hyperplanes. Suitable integral operators of Berndtsson–Andersson type are constructed
and estimated for this purpose.
Received: 7 July 2000 相似文献
15.
Z. Robinson 《Journal of Number Theory》2006,116(2):474-482
Assume that K is a perfect field of characteristic p>0 that is complete with respect to an ultrametric valuation, and let X be a rigid analytic variety over K. Suppose that X is smooth and connected with respect to its Grothendieck topology. Let f be a (global) function on X the differential of which vanishes locally at some point of X; then f is the pth power of a (global) function. 相似文献
16.
Judith Brinkschulte 《manuscripta mathematica》2006,120(2):181-192
We show that the Hartogs phenomenon holds in minimal, weakly 2-pseudoconcave generic C R submanifolds of a Stein manifold with trivial normal bundle. We also prove some results concerning the local and/or global solvability of the tangential Cauchy-Riemann equations for smooth forms and currents on weakly q-pseudoconcave C R manifolds. 相似文献
17.
Giorgio Patrizio 《Advances in Mathematics》2010,223(1):174-197
A (bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point xo, so that: (a) it is a smooth solution on M?{xo} to the Monge-Ampère equation n(ddcu)=0; (b) xo is a singular point for u of logarithmic type and eu extends smoothly on the blow up of M at xo; (c) ddc(eu)>0 at any point of M?{xo}. This class of manifolds naturally includes all smoothly bounded, strictly linearly convex domains and all smoothly bounded, strongly pseudoconvex circular domains of Cn.A set of modular parameters for bounded manifolds of circular type is considered. In particular, for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form. It is also shown that the class of normalizing maps for an n-dimensional manifold M is a new holomorphic invariant with the following property: it is parameterized by the points of a finite dimensional real manifold of dimension n2 when M is a (non-convex) circular domain while it is of dimension n2+2n when M is a strictly linearly convex domain. New characterizations of the circular domains and of the unit ball are also obtained. 相似文献
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Erlend Fornæss Wold 《Mathematische Annalen》2008,340(4):775-780
Since a paper by Rosay and Rudin (Trans. Am. Math. Soc. 310, 47–86, 1988) there has been an open question whether all Fatou–Bieberbach domains are Runge. We give an example of a Fatou–Bieberbach
domain Ω in which is not Runge. The domain Ω provides (yet) a negative answer to a problem of Bremermann.
Supported by Schweizerische Nationalfonds grant 200021-116165/1. 相似文献
20.
D. Cerveau 《Bulletin des Sciences Mathématiques》2003,127(3):215-221
We prove that an holomorphic function defined in the neighborhood of an algebraic knot f−1(0)∩S(0,ε) in dimension ?3, can be extended along the hypersurface f−1(0)∩B(0,ε). As an application we give a new proof of the Malgrange's singular Frobenius theorem. 相似文献