Showing papers in "Tohoku Mathematical Journal in 1988"
TL;DR: In this article, a condition suffisante pour que a systeme se mette sous une forme normale d'un systeme hyperbolique-parabolique is defined.
Abstract: On considere le probleme aux valeurs initiales pour les systemes non lineaires d'ordre 2: w t +∑ j=1 n f j (w) x j =∑ i,j=1 n {G ij (w) w xj } x i ou G ij (w) sont des matrices m×m. On donne une condition suffisante pour que ce systeme se mette sous une forme normale d'un systeme hyperbolique-parabolique
167 citations
TL;DR: In this paper, a variete de Riemann de contact de courbure φ-sectionnelle constante H.Riemann et al. satisfait Ric(X,X)+Ric(φX, φX)≤3n−1+(n+1)H pour chaque vecteur unite X∈T x M x∈M, tels que η(X)=0.
Abstract: Soit (M, η,g) une variete de Riemann de contact de courbure φ-sectionnelle constante H. Alors les courbures de Ricci satisfont Ric(X,X)+Ric(φX, φX)≤3n−1+(n+1)H pour chaque vecteur unite X∈T x M x∈M, tels que η(X)=0. L'egalite est vraie pour tout x∈M et pour un vecteur unite X∈T x M tel que η(X)=0, si et seulement si (M, η, g) est sasakienne
156 citations
TL;DR: In this article, the authors give a simplified proof of a recent result due to K. Masuda concerning the global existence and asymptotic behavior of non-negative solutions to some reaction-diffusion systems.
Abstract: We give a simplified proof of a recent result due to K. Masuda concerning the global existence and asymptotic behavior of non-negative solutions to some reaction-diffusion systems. This new method also provides an analogous result under weaker growth assumptions on the nonlinear terms. Introduction. Let Ω be an open, bounded domain of class C1 in Rn, with boundary Γ — dΩ. Let dlf d2 be two positive constants with dγ Φ d2 and a^x), a2{x) two nonnegative functions of class C\Γ) with a^^l, a2 tί 1. Let φeC\R+) be a nonnegative function. We consider the reaction-diffusion system (du/dt — dλAu + uφ{v) = 0 on R+xΩ \dv/dt — d2Δv — uφ{v) = 0 on R+xΩ with the homogeneous boundary conditions {aβu/dn + (1 - aλ)u = 0 on R+xΓ (2)
75 citations
TL;DR: In this paper, the authors consider a harmonic Kahler foliation and study the infinitesimal automorphisms of the foliation which are either transversally holomorphic or transversal Killing.
Abstract: Summary. In this paper we consider a harmonic Kahler foliation &~ and study the infinitesimal automorphisms of <&~ which are either transversally holomorphic or transversally Killing. A special study is made for the case of foliations with constant transversal scalar curvature.
46 citations
39 citations
TL;DR: In this article, an analogue quaternionique kahlerien des connexions auto-duales and anti-auto-duale is presented. Butler et al. construit une correspondance naturelle entre un fibre vectoriel avec de telles connexion and l'ensemble des fibres vectoriels d'Einstein hermitiens sur Z
Abstract: On donne un analogue quaternionique kahlerien des connexions auto-duales et anti-auto-duales. On construit une correspondance naturelle entre un fibre vectoriel avec de telles connexions et l'ensemble des fibres vectoriels d'Einstein hermitiens sur Z
36 citations
30 citations
28 citations
TL;DR: On demontre l'existence de solutions faibles possedant les epoques de propriete de regularite dans des domaines non bornes autres que l'espace R 3 tout entier as mentioned in this paper.
Abstract: On demontre l'existence de solutions faibles possedant les epoques de propriete de regularite dans des domaines non bornes autres que l'espace R 3 tout entier
22 citations
21 citations
TL;DR: In this article, it was shown that the transfinite α-modulus of the Teichmϋller ring is equal to the conformal modulus of a condenser in p-space.
Abstract: The authors prove the equality of the transfinite α-modulus and the discrete α-modulus of a condenser in p-space, 0 3. Two extremal properties for the transfinite modulus of the Teichmϋller ring are deduced from an expansion-con traction property of condensers. For the important examples of the spherical annulus and a ring of Grδtzsch type in p-space, p^S, the transfinite p-modulus is compared with the conformal modulus. 1. Introduction. In this paper we prove equality of the transfinite α-modulus and the discrete α-modulus (defined in §2) of a condenser in the finite p-space Rp, p ^ 3, 0 3, we show that the transfinite p-modulus is less than the conformal modulus but that their difference is bounded, whereas the two are equal in the plane (B2). We also study the ratios of the transfinite p-moduli of these condensers to their conformal moduli. Some of these results are analogues of theorems proved by Bagby ((Bl), (B2)) for the case p = a = 2 and by the present authors (AV3) for the case a = 2, p ;> 3. For p ^ 3, we let Rp denote the p-dimensional Euclidean space, and Rp its one-point compactification JRPU{°°}. By a condenser in Rp we shall mean an ordered pair (A, B) of nonempty, disjoint, compact subsets of Rp such that oo g A. In particular, it is not required that the complement of AUB be connected. We shall say that (A, B) is a condenser in Rp if A and B are subsets of Rp. The sets A and B are called plates of the condenser. If A, B, and R = Rp \(A\JB) are each connected, then the condenser is called a ring. If (A, B) and (A\ B') are two condensers in Rp such that Ac:A' and BaB' we shall say that (A, B)a(A', B').
TL;DR: In this paper, Schrodinger's operateur D avec un potentiel vecteur and a potentiel scalaire, who opere sur C ∞ (E), l'espace des sections c ∞ de E, etudie les effets de la connexion sur le spectre de D pour un fibre de lignes sur l'space projectif complexe CP n.
Abstract: Soit π:E→(M,g) un fibre ligne hermitien C ∞ sur une variete de Riemann C ∞ . On considere l'operateur de Schrodinger D avec un potentiel vecteur et un potentiel scalaire, qui opere sur C ∞ (E), l'espace des sections C ∞ de E. On etudie les effets de la connexion sur le spectre de D pour un fibre de lignes sur l'espace projectif complexe CP n
TL;DR: Theoretically, the Sobolev type in potential theory can be seen as the basis of modern potential theory, see as mentioned in this paper for a discussion of potential theory in the Dirichlet space.
Abstract: spaces of several variables, Acta Math. 129 (1972),137-193.[3] K. HANSSON, Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45(1979), 77-102.[4] J. L. JOURNE, Calderόn-Zygmund operators, pseudo-differential operators and the Cauchyintegral of Calderόn, Lecture Notes in Math., 994, Springer-Verlag, Berlin, Heidelberg,New York, Tokyo, 1983.[5] N. S. LANDKOF, Foundations of modern potential theory, Springer-Verlag, Berlin, Heidel-berg, New York, Tokyo, 1972.[ 6 ] D. A. STEGENGA, Multipliers of the Dirichlet space, Illinois J. of Math. 24 (1980), 113-119.
TL;DR: In this paper, the problem of generalizing Nevanlinna's theory of meromorphic functions has been studied and an elementary and simple method for generalizing Theorem A has been proposed.
Abstract: The method he used in the proof of Theorem A is very complicated and not suitable in generalizing Theorem A. The purpose of this paper is to decide permutable functions of a class of entire functions satisfying certain differential equation and to indicate an elementary and simple method by which we can generalize Theorem A. We assume that the reader is familiar with the fundamental concepts in Nevanlinna's theory of meromorphic functions, in particular, with symbols m{r, /) , T(r, /) and M(r, f) etc. (see [4]).
TL;DR: On etablit quelques inegalites relatives a la croissance des valeurs moyennes des fonctions holomorphes as discussed by the authors, et al.
Abstract: On etablit quelques inegalites relatives a la croissance des valeurs moyennes des fonctions holomorphes
TL;DR: On etudie la geometrie differentielle des feuilletages de codimension un totalement geodesiques admettant un champ de killing as discussed by the authors.
Abstract: On etudie la geometrie differentielle des feuilletages de codimension un totalement geodesiques admettant un champ de Killing