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Mathematische Zeitschrift, ISSN 0025-5874, 12/2014, Volume 278, Issue 3, pp. 769 - 793
We carry out a detailed study of $$\Xi ^+$$ Ξ + , a distinguished $$G$$ G -invariant Stein domain in the complexification of an irreducible Hermitian symmetric... 
Lie group complexification | Hermitian symmetric space | 32M05 | Mathematics, general | Mathematics | 32Q28 | Invariant Stein domain | MATHEMATICS | GEOMETRY
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 11, pp. 2511 - 2543
We prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, every closed discrete subset of a reduced Stein... 
Stein manifolds | Holomorphic functions | 1-Convex manifolds | Critical points | Stein spaces | Stratifications | MATHEMATICS, APPLIED | stratifications | COMPLEX-SPACES | INVARIANT | RIEMANN SURFACES | C-2 | critical points | CURVES | MATHEMATICS | 1-convex manifolds | MANIFOLDS | DOMAINS | Mathematics - Complex Variables
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2012, Volume 57, Issue 10, pp. 1073 - 1085
Let Ω be a smooth bounded pseudoconvex domain in ℂ n . We give several characterizations for the closure of Ω to have a Stein neighbourhood basis in the sense... 
pseudoconvex domains | Primary 32W05 | Stein neighbourhood basis | Neumann problem | Secondary 32A38 | MATHEMATICS | (partial derivative)over-bar-Neumann problem | PLURISUBHARMONIC DEFINING FUNCTIONS | OPERATOR | REGULARITY | PROPERTY | DERIVATIVE-NEUMANN PROBLEM | COMPLEX-VARIABLES | Complex variables | Maps | Boundaries | Mathematical analysis | Closures | Invariants
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 6, pp. 1077 - 1082
Let Gi be a closed Lie subgroup of U(n), Ωi be a bounded Gi-invariant domain in Cn which contains 0, and (9(Cn)Gi = C, for i= 1,2. If f : f21 →2 is... 
invariant domain | MATHEMATICS | MATHEMATICS, APPLIED | PROPER HOLOMORPHIC MAPPINGS | CIRCULAR DOMAINS | BERGMAN-KERNEL | biholomorphic mapping | degree of polynomial mapping | AUTOMORPHISMS | group action | Bergman kernel | STEIN-SPACES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2018, Volume 335, pp. 878 - 895
A question in low-dimensional symplectic topology asks whether every compact contractible 4-manifold admits the structure of a Stein domain. A related... 
Brieskorn sphere | Stein domain | Contractible | TIGHT CONTACT STRUCTURES | TOPOLOGY | MATHEMATICS | FOLIATIONS | SEIBERG-WITTEN INVARIANTS | SMALL SEIFERT MANIFOLDS | 3-MANIFOLDS | 4-MANIFOLDS | HOMOLOGY
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2016, Volume 66, Issue 1, pp. 143 - 174
In this paper we investigate invariant domains in Xi(+), a distinguished G-invariant, Stein domain in the complexification of an irreducible Hermitian... 
Lie group complexification | Hermitian symmetric space | Envelope of holomorphy | Invariant Stein domain | invariant Stein domain | MATHEMATICS | envelope of holomorphy | REPRESENTATIONS | EXTENSIONS | DOMAINS | GEOMETRY
Journal Article
by Xu, LH
ANNALS OF APPLIED PROBABILITY, ISSN 1050-5164, 02/2019, Volume 29, Issue 1, pp. 458 - 504
Let n is an element of N, let zeta(n,1), . . . , zeta(n,n) be a sequence of independent random variables with E zeta(n,i) = 0 and E vertical bar... 
Stable approximation | RATES | INVARIANT-MEASURES | L-1 discrepancy | Stein's method | normal domain of attraction of stable law | Wasserstein-1 distance (W-1 distance) | EXCHANGEABLE PAIRS | CONVERGENCE | STATISTICS & PROBABILITY | alpha-stable processes | RANDOM-VARIABLES
Journal Article
Geometry and Topology, ISSN 1465-3060, 12/2018, Volume 22, Issue 7, pp. 4307 - 4380
We recently defined invariants of contact 3-manifolds using a version of instanton Floer homology for sutured manifolds. In this paper, we prove that if... 
FLOER HOMOLOGY | MATHEMATICS | INSTANTON HOMOLOGY | LEFSCHETZ FIBRATIONS | COHOMOLOGY | INVARIANTS | CONTACT STRUCTURES | VARIETIES | DEHN SURGERY | KNOTS | SURFACES
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 12/2008, Volume 238, Issue 2, pp. 275 - 330
Let G/K be a noncompact, rank-one, Riemannian symmetric space, and let G(C) be the universal complexification of G. We prove that a holomorphically separable,... 
Riemann domain | Symmetric space | Semisimple Lie group | MATHEMATICS | LIE-GROUPS | semisimple Lie group | ENVELOPES | HOLOMORPHIC EXTENSIONS | symmetric space | INVARIANT DOMAINS | STEIN-SPACES | GEOMETRY
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2014, Volume 78, Issue 1, pp. 34 - 58
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 02/2013, Volume 24, Issue 2, pp. 1350004 - 1350038
We determine the contact homology algebra of a subcritical Stein-fillable contact manifold whose first Chern class vanishes. We also compute the genus-0 one... 
Contact homology | symplectic field theory | subcritical Stein manifolds | gravitational descendants | SYMPLECTIC FIELD-THEORY | MATHEMATICS | CONTACT | GROMOV-WITTEN THEORY | HOMOLOGY | Manifolds | Mathematical analysis | Homology | Mathematical models | Correlators | Complement | Invariants | Contact
Journal Article
manuscripta mathematica, ISSN 0025-2611, 05/2006, Volume 120, Issue 1, pp. 1 - 25
Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood Ω of the zero section where... 
Geometry | Topological Groups, Lie Groups | Mathematics, general | Algebraic Geometry | Calculus of Variations and Optimal Control | Mathematics | Number Theory | Optimization | MATHEMATICS | COMPLEXIFICATIONS | REPRESENTATIONS | HOLOMORPHIC EXTENSIONS | GRAUERT TUBES | INVARIANT DOMAINS | STEIN EXTENSIONS | GEOMETRY
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 1999, Volume 49, Issue 1, pp. 177 - 225
Let M = G/H be a real symmetric space and g = h + q the corresponding decomposition of the Lie algebra. To each open H-invariant domain D-q subset of or equal... 
Complex semigroup | Stein manifold | Convex function | Lie group | Subharmonic function | Envelope of holomorphy | Lie algebra | Invariant cone | MATHEMATICS | envelope of holomorphy | invariant cone | subharmonic function | convex function | complex semigroup
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 10/2014, Volume 24, Issue 4, pp. 2124 - 2134
We show that for any bounded domain $\varOmega\subset\mathbb{C} ^{n}$ of 1-type 2k which is locally convexifiable at p∈bΩ, having a Stein neighborhood basis,... 
Mathematics | Abstract Harmonic Analysis | Invariant metrics and pseudodistances | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Strongly pseudoconvex domains | Finite type | Differential Geometry | Dynamical Systems and Ergodic Theory | Holomorphic mappings | 32H02, 32E30 | 32T25 | MATHEMATICS
Journal Article
Magnetic Resonance Imaging, ISSN 0730-725X, 2016, Volume 34, Issue 8, pp. 1128 - 1140
Journal Article
Russian Mathematical Surveys, ISSN 0036-0279, 08/1999, Volume 54, Issue 4, pp. 729 - 752
In the paper, the relationship between the theory of holomorphic functions on two-dimensional complex manifolds and their differential topology is described.... 
MATHEMATICS | CONTACT STRUCTURES | REAL SURFACES | ALGEBRAIC APPROXIMATIONS | STEIN DOMAINS | SEIBERG-WITTEN INVARIANTS
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2017, Volume 67, Issue 6, pp. 2426 - 2462
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2012, Volume 62, Issue 5, pp. 1983 - 2011
In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of... 
Rosenlicht quotient | Invariant meromorphic function | Stein space | Lie group action | MATHEMATICS | invariant meromorphic function | MANIFOLDS | ALGEBRAIC GROUPS | ABBILDUNGEN KOMPLEXER RAUME | REDUCTIVE GROUP | Mathematics - Complex Variables
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 15
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 03/2020, Volume 278, Issue 4, p. 108341
We study the behaviour on rearrangement-invariant (r.i.) spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal... 
Integral operators | Optimality | Rearrangement-invariant spaces | INTERPOLATION | MATHEMATICS | OPTIMAL DOMAIN | SOBOLEV EMBEDDINGS | WEIGHTED NORM INEQUALITIES | IMBEDDING THEOREMS | HILBERT TRANSFORM | LITTLEWOOD MAXIMAL-FUNCTION | Mathematics - Functional Analysis
Journal Article
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