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Singular holomorphic functions for which all fibre-integrals are smooth

100%

Barlet D., Maire H.-M.

Annales Polonici Mathematici

2000

tom 74

nr 1

65-77

For a germ (X,0) of normal complex space of dimension n + 1 with an isolated singularity at 0 and a germ f: (X,0) → (ℂ,0) of holomorphic function with df(x) ≤ 0 for x ≤ 0, the fibre-integrals $s ↦ ∫_{f=s} ϱ ω' ⋀ \bar{ω''}, ϱ ∈ C^{∞}_{c}(X), ω', ω'' ∈ Ω_{X}^{n}$, are $C^{∞}$ on ℂ* and have an asymptotic expansion at 0. Even when f is singular, it may happen that all these fibre-integrals are $C^{∞}$. We study such maps and build a family of examples where also fibre-integrals for $ω',ω'' ∈ ⍹_{X}$, the Grothendieck sheaf, are $C^{∞}$.

Convergence of holomorphic chains

100%

Rams S.

Annales Polonici Mathematici

1996-1997

tom 65

nr 3

227-234

We endow the module of analytic p-chains with the structure of a second-countable metrizable topological space.

Some Results on Maps That Factor through a Tree

88%

Züst R.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than 2/3, the map factors through a tree.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Analysis and Geometry in Metric Spaces

1 Barlet D.

1 Maire H.-M.

1 Rams S.

1 Züst R.

1 2015

1 2000

1 1997

Wyniki wyszukiwania

Singular holomorphic functions for which all fibre-integrals are smooth

Convergence of holomorphic chains

Some Results on Maps That Factor through a Tree