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Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics

David M J. Calderbank, Henrik Pedersen (2000)

Annales de l'institut Fourier

We study the Jones and Tod correspondence between selfdual conformal 4 -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3 -manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kähler metrics and hypercomplex structures with symmetry. We also show that in the presence...

Semicompleteness of homogeneous quadratic vector fields

Adolfo Guillot (2006)

Annales de l’institut Fourier

We investigate the quadratic homogeneous holomorphic vector fields on  C n that are semicomplete, this is, those whose solutions are single-valued in their maximal definition domain. To a generic quadratic vector field we rationally associate some complex numbers that turn out to be integers in the semicomplete case, thus showing that the linear equivalence classes of semicomplete vector fields are contained in some sort of lattice in the space of linear equivalence classes of quadratic ones. We prove...

Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).

C. H. Chang, H. P. Lee (1999)

Publicacions Matemàtiques

Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn-m ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z1, ..., zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂b closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂b if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies Lp estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.

Semi-groupe de Lie associé à un cône symétrique

Khalid Koufany (1995)

Annales de l'institut Fourier

Soit V une algèbre de Jordan simple euclidienne de dimension finie et Ω le cône symétrique associé. Nous étudions dans cet article le semi-groupe Γ , naturellement associé à V , formé des automorphismes holomorphes du domaine tube T Ω : = V + i Ω qui appliquent le cône Ω dans lui-même.

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in ℝ n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of ℝ n , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

Semi-simple Carrousels and the Monodromy

David B. Massey (2006)

Annales de l’institut Fourier

Let 𝒰 be an open neighborhood of the origin in ℂ n + 1 and let f : ( 𝒰 , 0 ) → ( ℂ , 0 ) be complex analytic. Let z 0 be a generic linear form on ℂ n + 1 . If the relative polar curve Γ f , z 0 1 at the origin is irreducible and the intersection number ( Γ f , z 0 1 · V ( f ) ) 0 is prime, then there are severe restrictions on the possible degree n cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when ( Γ f , z 0 1 · V ( f ) ) 0 is not prime.

Semistable quotients

Peter Heinzner, Luca Migliorini, Marzia Polito (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Separately radial and radial Toeplitz operators on the projective space and representation theory

Raul Quiroga-Barranco, Armando Sanchez-Nungaray (2017)

Czechoslovak Mathematical Journal

We consider separately radial (with corresponding group 𝕋 n ) and radial (with corresponding group U ( n ) ) symbols on the projective space ℙ n ( ℂ ) , as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the C * -algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...

Separately superharmonic functions in product networks

Victor Anandam (2015)

Annales Polonici Mathematici

Let X×Y be the Cartesian product of two locally finite, connected networks that need not have reversible conductance. If X,Y represent random walks, it is known that if X×Y is recurrent, then X,Y are both recurrent. This fact is proved here by non-probabilistic methods, by using the properties of separately superharmonic functions. For this class of functions on the product network X×Y, the Dirichlet solution, balayage, minimum principle etc. are obtained. A unique integral representation is given...

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