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Let B be the open unit ball for a norm on $ℂ^{n}$ . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on $ℂ^{n}$ . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

A characterization of non-hyperelliptic Jacobi varieties.

G.E. Welters (1983)

Inventiones mathematicae

A characterization of proper regular mappings

T. Krasiński, S. Spodzieja (2001)

Annales Polonici Mathematici

Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.

A characterization of quasi-homogeneous Gorenstein surface singularities

Jonathan M. Wahl (1985)

Compositio Mathematica

A characterization of short curves of a Teichmüller geodesic.

Rafi, Kasra (2005)

Geometry & Topology

A Characterization of the Ball by its Intrinsic Metrics.

Charles M. Stanton (1983)

Mathematische Annalen

A characterization of the complex affine line.

W. Kucharz (1996)

Manuscripta mathematica

A Characterization of the Polydisc.

Charles M. Stanton (1980)

Mathematische Annalen

A characterization of totally real generic submanifolds of strictly pseudoconvex boundaries in Cn admitting a local foliation by interpolation submanifolds.

Andrei Iordan (1990)

Mathematische Annalen

A Class of Compact Complex Manifolds with Negative Tangent Bundles.

Bun Wong (1984)

Mathematische Zeitschrift

A class of functions containing polyharmonic functions in ℝⁿ

V. Anandam, M. Damlakhi (2003)

Annales Polonici Mathematici

Some properties of the functions of the form $v (x) = \sum_{i = 0}^{m} {| x |}^{i} h_{i} (x)$ in ℝⁿ, n ≥ 2, where each $h_{i}$ is a harmonic function defined outside a compact set, are obtained using the harmonic measures.

A class of integral operators on mixed norm spaces in the unit ball

Songxiao Li (2007)

Czechoslovak Mathematical Journal

This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.

A class of maximal plurisubharmonic functions

Azimbay Sadullaev (2012)

Annales Polonici Mathematici

We consider a class of maximal plurisubharmonic functions and prove several properties of it. We also give a condition of maximality for unbounded plurisubharmonic functions in terms of the Monge-Ampère operator $(d d^{c} e^{u}) ⁿ$ .

A class of non-algebraic threefolds

Matei Toma (1989)

Annales de l'institut Fourier

Let $X$ be a compact complex nonsingular surface without curves, and $E$ a holomorphic vector bundle of rank 2 on $X$ . It turns out that the associated projective bundle $P E$ has no divisors if and only if $E$ is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.

A class of non-rational surface singularities with bijective Nash map

Camille Plénat, Patrick Popescu-Pampu (2006)

Bulletin de la Société Mathématique de France

Let $(𝒮, 0)$ be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor $E$ and its irreducible components $E_{i}$ , $i \in I$ . The Nash map associates to each irreducible component $C_{k}$ of the space of arcs through $0$ on $𝒮$ the unique component of $E$ cut by the strict transform of the generic arc in $C_{k}$ . Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if $E \cdot E_{i} < 0$ for any $i \in I$ .

A classification of strictly pseudoconcave homogeneous manifolds

A. T. Huckleberry, D. Snow (1981)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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