Showing papers in "Tohoku Mathematical Journal in 1996"
TL;DR: The log smooth deformation functor has a representable hull as mentioned in this paper, which is a generalization of the logarithmic deformation theory introduced by Kawamata and Namikawa.
Abstract: This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for example, the following two types of deformations: (1) relative deformations of a certain kind of a pair of an algebraic variety and a divisor of it, and (2) global smoothings of normal crossing varieties. The former is a generalization of the relative deformation theory introduced by Makio, and the latter coincides with the logarithmic deformation theory introduced by Kawamata and Namikawa.
150 citations
TL;DR: In this article, a periodic strong solution of the Navier-Stokes equations for the prescribed external force in unbounded domains is constructed, and the solution is shown to be strong.
Abstract: We shall construct a periodic strong solution of the Navier-Stokes equations for the prescribed external force in unbounded domains.
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TL;DR: In this article, the authors characterize a class of hyperbolic cylinders of the de Sitter spacetime as the only complete non-compact spacelike hypersurfaces with constant lowest mean curvature and having more than one topological end.
Abstract: We characterize a class of hyperbolic cylinders of the de Sitter spacetime as the only complete non-compact spacelike hypersurfaces with constant lowest mean curvature and having more than one topological end.
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TL;DR: In this article, it was shown that the Bergman kernel function associated to pseudoconvex domains of finite type with the property that the Levi form of the boundary has at most one degenerate eigenvalue, is a standard kernel of Calderon-Zygmund type with respect to the Lebesgue measure.
Abstract: We show that the Bergman kernel function, associated to pseudoconvex domains of finite type with the property that the Levi form of the boundary has at most one degenerate eigenvalue, is a standard kernel of Calderon-Zygmund type with respect to the Lebesgue measure. As an application, we show that the Bergman projection on these domains preserves some of the Lebesgue classes.
TL;DR: In this paper, the authors consider periodic, infinite delay differential equations and investigate dissipativeness for these equations, and prove Massat's theorem from this weakness in an elementary way, and then they extend a theorem of Pliss giving a necessary and sufficient condition for this weak dissipation.
Abstract: We consider periodic, infinite delay differential equations. We investigate dissipativeness for these equations. Massat proved that dissipative, periodic, infinite delay equations have a periodic solution. For our purpose we need a weaker dissipativeness, so we prove Massat's theorem from this weak dissipativeness in an elementary way. Then we extend a theorem of Pliss giving a necessary and sufficient condition for this weak dissipativeness. We also present a theorem using Liapunov functionals to show the weak dissipativeness and hence the existence of a periodic solution.
TL;DR: In this paper, the authors studied conformal vector fields on pseudo-Riemannian nian manifolds which are locally gradient fields and obtained global solutions of the oscillator and peandulum equation for the Hessian of this function on a pseudo-riemanni manifold.
Abstract: We study conformal vector fields on pseudo-Rieman nian manifolds which are locally gradient fields. This is closely related with a certain differential equation for the Hessian of a real function. We obtain global solutions of the oscillator and peandulum equation for the Hessian of this function on a pseudo-Riemannian manifold, generalizing previous results by M. Obata, Y. Tashiro, and Y. Kerbrat. In particular, it turns out that the pendulum equation characterizes a certain conformal type of metrics carrying a conformal vector field with infinitely many zeros. 1. Introduction. Conformal mappings and conformal vector fields are classical topics in geometry. Essential conformal vector fields on Riemannian spaces were studied by Obata, Lelong-Ferrand and Alekseevskii (Al), (La2). Conformal gradient fields are essentially solutions of the differential equation V2φ = (Aφ/n) g. This equation was studied since the 1920's by Brinkmann, Fialkow, Yano, Tashiro, Kerbrat and others. In the Riemannian case the results are quite complete. In the pseudo-Riemannian case a systematic approach has started in our previous paper (KR2) including a conformal classification theorem. A classical result by Obata and Tashiro characterizes the standard sphere as the only complete Riemannian manifold admitting a non-constant solution of the equation V2φ= —c2φg for a non-zero constant c. This is nothing but the classical harmonic oscillator equation. In Section 3 we study the following generalization: given a function h: R-+R, the conformal gradient field equation V2φ + h(φ) g = 0 imposes very strong conditions on the underlying pseudo-Riemannian manifold. We give analogous results for the case of the equation of the general undamped oscillator. This illustrates how a metric can be modeled within a conformal class by a second order differential equation. The metric in this case is completely determined by the equation and the choice of a constant of integration which is essentially the energy of the undamped oscillator. Similarly, for small energy, the pendulum equation on a pseudo-Riemannian manifold determines the metric uniquely. In the Riemannian case it is conformal to the standard sphere whereas in the case of an indefinite metric it is conformal to a noncompact manifold M(Z). This manifold carries a conformal gradient field with infinitely many zeros. A short announcement of the results in this paper appeared in (KR3).