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Showing papers in "Tohoku Mathematical Journal in 1990"


Journal ArticleDOI
TL;DR: In this article, the authors prove a representation formula for spacelike surfaces with prescribed mean curvature in terms of their Gauss maps, where the Gauss map G is defined to be a mapping of M into the unit pseudosphere H in L 3, which assigns to each point p of M the point in H obtained by translating the timelike unit normal vector at p to the origin.
Abstract: For an oriented spacelike surface in Minkowski 3-space L 3 , the Gauss map G is defined to be a mapping of M into the unit pseudosphere H in L 3 , which assigns to each point p of M the point in H obtained by translating the timelike unit normal vector at p to the origin. Our primary object of this paper is to prove a representation formula for spacelike surfaces with prescribed mean curvature in terms of their Gauss maps

133 citations


Journal ArticleDOI
TL;DR: In this article, the notion of polarizable Hodge Modules on complex analytic spaces was introduced, which corresponds philosophically to that of pure perverse sheaves in characteristic p [BBD].
Abstract: Introduction. In [S1], [S2] we introduced the notion of polarizable Hodge Modules on complex analytic spaces, which corresponds philosophically to that of pure perverse sheaves in characteristic p [BBD]. If X is smooth, MH(X,n)p the category of polarizable Hodge Modules of weight n (and with k-structure) is a full subcategory of the category of filtered holonomic •¬x-Modules (M,F) with k-structure by a given isomorphism ƒ¿ : DR(M)•¬C•¬k K for a perverse sheaf K (defined over k). Here k is a subfield of R, and we assume for simplicity k=R in this note. In general MH(X,n)p is defined using local embeddings into smooth varieties, and the underlying perverse sheaves K are

92 citations






Journal ArticleDOI
TL;DR: In this article, the authors presented a method to construct solutions with internal transition layers in the context of singular perturbation problems, and they also emphasized the stability analysis of the solutions obtained as above.
Abstract: It is the purpose of this paper to present a method to construct solutions with internal transition layers in the context of singular perturbation problems. We also emphasize the stability analysis of the solutions so obtained as above. Our method is slightly different from those in [5], [6], [12], [13] in that existence and stability analysis are carried out simultaneously

36 citations






Journal ArticleDOI
Qing Liu1
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.cedram.php) of the agreement are discussed, i.e., every copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract: © Université Bordeaux 1, 1989, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.


Book ChapterDOI
TL;DR: In this paper, it was shown that Husimi's theorem does not hold for relatively complemented lattices with a negation and that the chain law holds for every sublattice closed with respect to a relative negation.
Abstract: In a paper on the foundation of quantum mechanics, Kodi Husimi(1) conjectured that a lattice with a negation is modular if the chain law holds for every sublattice closed with respect to relative negation. Although the theorem in this form does not hold, as we show by an example, we prove a theorem of a similar nature for relatively complemented lattices.






Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic behavior of the gradient flow of the Yang-Mills functional near Yang-mills connections, and showed that the gradient flows of the functional near the Yangmills functional can be characterized as follows:
Abstract: The purpose of this paper is to study the asymptotic behavior of the gradient flow of the Yang-Mills functional near Yang-Mills connections








Journal ArticleDOI
TL;DR: In this article, it was shown that a superminimal immersion of a Riemann surface in a Euclidean space with constant curvature is rigid, even in R^>R.
Abstract: 0. Introduction. The rigidity aspects of minimal hypersurfaces in a Euclidean space or a sphere have constantly drawn authors' attentions, about which we mention the recent conclusive result of Dajczer-Gromoll [12] which states that a complete minimally immersed hypersurface of dimension >4 in S, or in R if it dose not contain R~ as a factor, is rigid, even in R^>R. On the other hand the failure of this theorem to hold in general for a Riemann surface is well-known, to which we should add the positive result of Barbosa [2] which says that a minimally immersed Riemann sphere in a sphere is rigid, that of Choi-Meeks-White [11] which asserts that a properly embedded minimal surface in R with more than one end is rigid, and that of Ramanathan [22] stating that for each compact Riemann surface minimally immersed in S, there are only finitely many other minimal immersions isometric to it. Along another line of development, minimal immersions (especially the superminimal ones) of Riemann surfaces into CP have recently been extensively studied by several authors [6], [8], [13], [14], [15], [25]. It is the purpose of this paper to look into the rigidity problem for superminimal immersions of compact Riemann surfaces into CP; to the author's knowledge the only results of this kind are the rigidity theorem of Calabi [7] which says that a holomorphic curve (a special class of superminimal immersions) in CP is rigid, the rigidity of totally real superminimal immersions in CP in Bolton-Jensen-Rigoli-Woodward [3], and the rigidity of superminimal immersions of constant curvature in [3], Bando-Ohnita [4], and [10]. One different feature of minimal immersions of Riemann surfaces into CP from those into S is that the immersion is of (real) codimension 2, with respect to which the conclusion of rigidity would be harder to draw in general. However with the given holomorphic data which a superminimal immersion in CP enjoys, we are able to assert the rigidity for large classes of superminimal immersions. After some preliminaries in § 1 on the structure of minimal immersions in CP through the work in Chern-Wolfson [8], [9], and Eschenberg-Gaudalupe-Tribuzy [15], we establish the result (Lemma 1) in §2 that infers that those points of a given superminimal immersion at which the curvature K—A are exactly those ramified points of index > 2 of either the holomorphic curve or the dual of the holomorphic curve (but