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Volume 47 (1995)
- Issue 4 Pages 441-
- Issue 3 Pages 297-
- Issue 2 Pages 151-
- Issue 1 Pages 1-
Predecessor
Volume 47, Issue 2
Displaying 1-7 of 7 articles from this issue
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KLAUS ALTMANN1995 Volume 47 Issue 2 Pages 151-184
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSWe investigate those deformations of affine toric varieties (toric singularities) that arise from embedding them into higher dimensional toric varieties as a relative complete intersection. On the one hand, many examples promise that these so-called toric deformations cover a great deal of the entire deformation theory. On the other hand, they can be described explicitly. Toric deformations are related to decompositions (into a Minkowski sum) of cross cuts of the polyhedral cone defining the toric singularity. Finally, we consider the special case of toric Gorenstein singularities. Many of them turn out to be rigid; for the remaining examples the description of their toric deformations becomes easier than in the general case.View full abstractDownload PDF (1338K) -
BANG-YEN CHEN, FRANKI DILLEN, LEOPOLD VERSTRAELEN, LUC VRANCKEN1995 Volume 47 Issue 2 Pages 185-198
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSThe first author introduced in a previous paper an important Riemannian invariant for a Riemannian manifold, namely take the scalar curvature function and subtract at each point the smallest sectional curvature at that point. He also proved a sharp inequality for this invariant for submanifolds of real space forms.In this paper we study totally real submanifolds in the nearly Kahler six-sphere that realize the equality in that inequality.In this way we characterize a class of totally real warped product immersions by one equality involving their sectional curvatures.View full abstractDownload PDF (532K) -
E. NORMAN DANCER, ZONGMING GUO1995 Volume 47 Issue 2 Pages 199-225
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSIn this paper, we study the stability of changing sign solutions of weakly nonlinear second order elliptic equations. Here by stability, we means stability for the natural corresponding parabolic problem. We prove the instability of many sign changing solutions. On the other hand, we find a number of methods for obtaining stable changing sign solutions. Some of these methods involve singular perturbations.View full abstractDownload PDF (1104K) -
HITOSHI ISHII, PANAGIOTIS SOUGANIDIS1995 Volume 47 Issue 2 Pages 227-250
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSIn this note we study the generalized motion of noncompact hypersurfaces with normal velocity depending on the normal direction and the curvature tensor. This work extends the by-now-classical works of Evans and Spruck (for mean curvature) and Chen, Giga and Goto (for general motions with sublinear curvature dependence), because it allows general dependence on the curvature tensor. It also allows a general treatment of the generalized evolution including noncompact hypersurfaces. A number of results regarding no interior, convexity, etc. are also presented.View full abstractDownload PDF (831K) -
DAVID A. COX1995 Volume 47 Issue 2 Pages 251-262
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSThis paper describes the data needed to specify a map from a scheme to an arbitrary smooth toric variety. The description is in terms of a collection of line bundles and sections on the scheme which satisfy certain compatibility and nondegeneracy conditions. There is also a natural torus action on these collections. As an application, we show how homogeneous polynomials can be used to describe all maps from a pro-jective space (or more generally a toric variety) to a smooth complete toric variety.View full abstractDownload PDF (530K) -
PAUL ELOE, MUHAMMAD ISLAM1995 Volume 47 Issue 2 Pages 263-269
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSIntegrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.View full abstractDownload PDF (228K) -
SHIMURA CURVES AS INTERSECTIONS OF HUMBERT SURFACES AND DEFINING EQUATIONS OF QM-CURVES OF GENUS TWOKI-ICHIRO HASHIMOTO, NAOKI MURABAYASHI1995 Volume 47 Issue 2 Pages 271-296
Published: June 01, 1995
Released on J-STAGE: May 22, 2009
JOURNAL FREE ACCESSShimura curves classify isomorphism classes of abelian surfaces with quaternion multiplication. In this paper, we are concerned with a fibre space, the base space of which is a Shimura curve and fibres are curves of genus two whose jacobian varieties are abelian surfaces of the above type. We shall give an explicit defining equation for such a fibre space when the discriminant of the quaternion algebra is 6 or 10.View full abstractDownload PDF (789K)
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