Plurisubharmonic envelopes and supersolutions
نویسندگان
چکیده
منابع مشابه
Extremal Ω-plurisubharmonic Functions as Envelopes of Disc Functionals
For each closed, positive (1, 1)-current ω on a complex manifold X and each ω-upper semicontinuous function φ on X we associate a disc functional and prove that its envelope is equal to the supremum of all ω-plurisubharmonic functions dominated by φ. This is done by reducing to the case where ω has a global potential. Then the result follows from Poletsky’s theorem, which is the special case ω ...
متن کاملValuations and plurisubharmonic singularities
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 Polynomials and Bumping
We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain Ω ⊂ C in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with ∂Ω, at the site of the bumping, are explicitly realised. Generally, when Ω ⊂ C, n ≥ 3, the known methods lead to bumpings with high orders of contact — which are not explicitly know...
متن کاملMaximal 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...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2019
ISSN: 0022-040X
DOI: 10.4310/jdg/1571882428