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Barth-Lefschetz theorems for singular spaces.

Christian Okonek (1987)

Journal für die reine und angewandte Mathematik

Bernstein and De Giorgi type problems: new results via a geometric approach

Alberto Farina, Berardino Sciunzi, Enrico Valdinoci (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the form $div (a (| \nabla u (x) |) \nabla u (x)) + f (u (x)) = 0 .$ Our setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in $ℝ^{2}$ and $ℝ^{3}$ and of the Bernstein problem on the flatness of minimal area graphs in $ℝ^{3}$ . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...

Big Picard theorems for holomorphic mappings into the complement of $2 n + 1$ moving hypersurfaces in $ℂ P^{n}$ .

Nguyen Thi Thu Hang, Tran Van Tan (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Biholomorphic domains with inequivalent boundaries.

D.E. Barrett (1986)

Inventiones mathematicae

Biholomorphic invariants related to the Bergman functions [Book]

Maciej Skwarczyński (1980)

Biholomorphic mappings between bounded domains in Cn.

Yifei Pan (1996)

Manuscripta mathematica

Biholomorphic Mappings Between Certain Real Analytic Domains in C2.

Klas Diederich, John Eric Fornaess (1979)

Mathematische Annalen

Biholomorphic maps determined on the boundary

Nozomu Mochizuki (1977)

Annales de l'institut Fourier

Let $D$ be a bounded domain in $C^{n}$ such that the boundary $b D$ is topologically $S^{2 n - 1}$ in $R^{2 n}$ with a regular point; let $f : \tilde{D} \to C^{n}$ be a holomorphic map where $\tilde{D}$ is a neighborhood of $\overline{D}$ . If $f$ is one-to-one when restricted to $b D$ , then $f : D \to f (D)$ is biholomorphic.

Boundary Analyticity of Proper Holomorphic Maps of Domains with Non-Analytic Boundaries.

David E. Barrett (1983)

Mathematische Annalen

Boundary Behavior of Meromorphic Maps.

Giorgio Patrizio (1982)

Mathematische Annalen

Boundary Behavior of Proper Holomorphic Correspondences.

S. Bell, E. Bedford (1985)

Mathematische Annalen

Boundary Interpolation and Proper Holomorphic Maps from the Disc to the Ball.

Josip Globevnik (1988)

Mathematische Zeitschrift

Boundary Interpolation by Proper Holomorphic Maps.

Josip Globevnik (1987)

Mathematische Zeitschrift

Boundary Regularity of Proper Holomorphic Mappings.

Klas Diederich, John E. Fornaess (1982)

Inventiones mathematicae

B-regularity of certain domains in ℂⁿ

Nguyen Quang Dieu, Nguyen Thac Dung, Dau Hoang Hung (2005)

Annales Polonici Mathematici

We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.

Displaying 1 – 15 of 15

Biholomorphic invariants related to the Bergman functions [Book]

Currently displaying 1 – 15 of 15