Miyuki Koiso
Nara Women's University
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Featured researches published by Miyuki Koiso.
Siam Journal on Mathematical Analysis | 2007
Miyuki Koiso; Bennett Palmer
We consider capillary surfaces for certain rotationally invariant elliptic parametric functionals supported on two hydrophobically wetted horizontal plates separated by a fixed distance. It is shown that each such stable capillary surface is uniquely determined by the volume interior to the surface.
Manuscripta Mathematica | 1995
Miyuki Koiso
We generalize the classical Steiner symmetrization to surfaces with self-intersections. Then we apply the generalized Steiner symmetrization to several isoperimetric problems. For example, let Г⊂ℝ3 be an analytic plane Jordan curve which is symmetric with respect to a plane ϖ (ϖ⊅Г). LetS be a compact immersed surface bounded by Λ which has the smallest area among all compact surfaces bounded by Λ with a fixed volume. In this situation, under some additional assumptions, the wholeS is proved to be symmetric with respect to ϖ. When Λ is a round circle,S is proved to be a spherical cap or the flat disk bounded by Λ without any additional assumptions.
Advances in Calculus of Variations | 2015
Miyuki Koiso; Bennett Palmer; Paolo Piccione
Abstract We prove bifurcation results for (compact portions of) nodoids in ℝ3, whose boundary consists of two fixed coaxial circles of the same radius lying in parallel planes. Degeneracy occurs at an infinite discrete sequence of instants, that are divided into four classes. Different types of bifurcation and break of symmetry occur at each instant of three of the four classes; bifurcation does not occur at the degeneracy instants of the fourth class.
Proceedings of the American Mathematical Society | 2013
Miyuki Koiso; Bennett Palmer
We show that for an axially symmetric anisotropic surface energy, only stable disc-type surfaces with constant anisotropic mean curvature bounded by a circle which lies in a plane orthogonal to the rotation axis of the Wulff shape are rescalings of parts of the Wulff shape and the flat disc.
Archive | 2014
Miyuki Koiso
Surfaces with constant mean curvature (CMC surfaces) are critical points of the area functional among surfaces enclosing the same volume. Therefore, they are a simple example of solutions of variational problem with constraint. A CMC surface is said to be stable if the second variation of the area is nonnegative for all volume-preserving variations satisfying the given boundary condition. The purpose of this article is to show some fundamental methods to study the stability for CMC surfaces. Especially, we give a criterion on the stability for compact CMC surfaces with prescribed boundary. Another concept that is closely related to the stability for CMC surfaces is the so-called bifurcation. We give sufficient conditions on a one-parameter family of CMC surfaces so that there exists a bifurcation. Moreover, we give a criterion for CMC surfaces in the bifurcation branch to be stable.
Manuscripta Mathematica | 1989
Miyuki Koiso
We give a sufficient condition on a Jordan curve Γ in the 3-dimensional open hemisphereH ofS3 in terms of the Hopf fibering under which Γ spans a unique compact generalized minimal surface inH. The maximum principle for minimal surfaces inS3 is proved and plays an important role in the proof of the uniqueness theorem.
Indiana University Mathematics Journal | 2005
Miyuki Koiso; Bennett Palmer
Mathematische Zeitschrift | 1986
Miyuki Koiso
Tohoku Mathematical Journal | 2002
Miyuki Koiso
Calculus of Variations and Partial Differential Equations | 2007
Miyuki Koiso; Bennett Palmer