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Displaying similar documents to “An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid”

Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Enrico Bernardi, Antonio Bove, Vesselin Petkov (2010)

Journées Équations aux dérivées partielles

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We study a class of third order hyperbolic operators P in G = Ω ∩ { 0 ≤ t ≤ T } , Ω ⊂ ℝ n + 1 with triple characteristics on t = 0 . We consider the case when the fundamental matrix of the principal symbol for t = 0 has a couple of non vanishing real eigenvalues and P is strictly hyperbolic for t > 0 . We prove that P is strongly hyperbolic, that is the Cauchy problem for P + Q is well posed in G for any lower order terms Q .

Hyperbolic lattice-point counting and modular symbols

Yiannis N. Petridis, Morten S. Risager (2009)

Journal de Théorie des Nombres de Bordeaux

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For a cocompact group Γ of SL 2 ( ℝ ) we fix a real non-zero harmonic 1 -form α . We study the asymptotics of the hyperbolic lattice-counting problem for Γ under restrictions imposed by the modular symbols γ , α . We prove that the normalized values of the modular symbols, when ordered according to this counting, have a Gaussian distribution.

Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka, Luis Tovar (1996)

Banach Center Publications

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The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρ X α ( z 0 , z ) [ ] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Local coordinates for SL ( n , C ) -character varieties of finite-volume hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti (2012)

Annales mathématiques Blaise Pascal

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Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL ( 2 , C ) with the n -dimensional irreducible representation of SL ( 2 , C ) in SL ( n , C ) . In this paper we give local coordinates of the SL ( n , C ) -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

On the problem of symmetrization of hyperbolic equations

V. Kostin (1992)

Banach Center Publications

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The aspects of symmetrization of hyperbolic equations which will be considered in this review have their own history and are related to some classical results from other areas of mathematics ([12]). Here symmetrization means representation of an initial system of equations in the form of a symmetric t-hyperbolic system in the sense of Friedrichs. Some equations of mathematical physics, for example, the equations of acoustics, of gas dynamics, etc. already have this form. In the 70's...