منابع مشابه
Maximal Plurisubharmonic Models
An analytic pair of dimension n and center V is a pair (V,M) where M is a complex manifold of (complex) dimension n and V ⊂ M is a closed totally real analytic submanifold of dimension n. To an analytic pair (V,M) we associate the class U (V,M) of the functions u : M → [0,π/4[ which are plurisubharmonic in M and such that u(p)= 0 for each p ∈ V . If U (V,M) admits a maximal function u, the trip...
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We extend to higher dimension our valuative analysis of singularities of psh functions started in [FJ2]. Following [KoSo], we describe the geometry of the space V of all normalized valuations on C[z1, . . . , zn] centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of C n over the ...
متن کاملPlurisubharmonic Domination
A common device in several complex variables, notably in the theory of Stein spaces, is to exhaust a space S by a sequence of holomorphically convex compact subsets Kj . Analytical problems one has to solve on S (say, a Cousin problem) tend to become more manageable when restricted to Kj because over compact sets the data is uniformly controlled; on the other hand, once the problem is solved on...
متن کاملLocal inequalities for plurisubharmonic functions
The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of polynomial, algebraic and analytic functions. The paper has much in common with an earlier paper [Br] of the author.
متن کاملTangents of plurisubharmonic functions
Tangents of plurisubharmonic functions Local properties of plurisubharmonic functions are studied by means of the notion of tangent which describes the behavior of the function near a given point. We show that there are plurisubharmonic functions with several tangents, disproving a conjecture of Reese Harvey.
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2009
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x09005856