PRGC2011 Poster

The 10th Pacific RIM Geometry Conference 2011 Osaka-Fukuoka: Poster Session and Presentation

		Poster Session and Presentation
	Part I & II	Tatsuyoshi Hamada (Fukuoka University, Japan)
		“MathLibre: an open source project for enjoying mathematics with computer”
		Abstract: MathLibre is a new open source project offering many documents and mathematical software packages. MathLibre is the direct descendant project of “KNOPPIX/Math”. Once you run the live system, you can enjoy a wonderful world of mathematical software without needing to install anything yourself. We will demonstrate how to boot and use this system.

	Part I	Makoto Narita (Okinawa National College of Technology, Japan)
		“On gravitational collapse of five dimensional triaxial Bianchi-IX spacetimes with matter”
		Abstract: We prove that five dimensional spacetimes with matter developing from suitable asymptotically flat triaxial Bianchi-IX symmetric initial data and containing a trapped or marginally trapped three-surface necessarily possess a complete future null infinity. The past region of the null infinity in bounded to the future by a regular null hypersurface (event horizon), whose cross-sectional volume satisfies a Penrose-like inequality, relating it to the gravitational (final Bondi) mass.

	Part I	Masashi Yasumoto (Kobe University, Japan)
		“Construction of discrete constant mean curvature surfaces”
		Abstract: In the case for smooth surfaces, any constant mean curvature surface in R³ can be obtained by solving a certain differential equation, using a loop group splitting, and inserting one component of the splitting into a Sym-Bobenko formula. This recipe is called the DPW method. Also in the case for discrete surfaces, there exists a discrete analogue of the DPW method, which we briefly explain in this poster.

	Part I & II	Yuriko Umemoto (Osaka City University, Japan)
		“On the growth functions of hyperbolic Coxeter groups”
		Abstract: We will talk about the growth functions of the Coxeter groups, which are known to be rational functions. In particular we will study the distributions of poles of the growth functions of simplex hyperbolic Coxeter groups.

	Part I	Hassanien Samah Gaber Mohamed (Kobe University, Japan)
		“Inextensible flow of spacelike and timelike curves in de Sitter space S^2,1”
		Abstract: In this poster we will study the motion of spacelike and timelike curves in de Sitter space S^2,1. The evolution equations for curvature and torsion are given as a system of partial differential equations. In addition, we will study inextensible flow of spacelike and timelike curves in de Sitter space S^2,1, and we will get necessary and sufficient conditions for the flows of spacelike and timelike curves to be inextensible.

	Part I & II	Hisayoshi Muroya (OCAMI, Japan)
		“n-end catenoids of genus one”
		Abstract: An n-end catenoid is a complete minimal surface in the three-dimensional Euclidean space with finite total curvature and n catenoidal ends. We give a necessary and sufficient condition for the existence of an n-end catenoid of genus one. By using the condition, we construct several new examples.

	Part I & II	Xianfeng Wang (Nankai University, P. R. China)
		“Second eigenvalue of a Jacobi operator of hypersurfaces with constant scalar curvature”
		Abstract: Let x : M → Sⁿ⁺¹(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n−1)r, r ≥ 1, in a unit sphere Sⁿ⁺¹(1), n ≥ 5 and J_s be the Jacobi operator of M. In this case, the Jacobi operator J_s is given by J_s= −□− {n(n−1)H+nHS−f₃}, which is associated with the variational characterization of the hypersurfaces with constant scalar curvature in Sⁿ⁺¹(1), where f₃ = Σ_j=1ⁿk_j³ . The spectral behavior of J_s is directly related to the instability of hypersurfaces with constant scalar curvature. In 2004, L. J. Alías, A. Brasil and L. A. M. Sousa studied the first eigenvalue of J_s of the hypersurface with constant scalar curvature n(n−1) in Sⁿ⁺¹(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue of the Jacobi operator J_s of the hypersurface with constant scalar curvature n(n − 1)r, r > 1 in Sⁿ⁺¹(1). In this paper, we study the second eigenvalue of the Jacobi operator J_s of M and give an optimal upper bound for the second eigenvalue of J_s. This is joint work with Professor Haizhong Li.

	Part I & II	Ayaka Shimizu (OCAMI, Japan)
		“Region Select—a game using knot theory”
		Abstract: We introduce Region Select which is a game using knot theory. In this game we consider a knot projection on a display whose crossings have “lamps” which can be turned on or off by clicking on the region bordering it. The goal of this game is to light up all of the lamps by clicking on regions. In this poster, we show that we can complete the game for any knot projection with lamps by considering “region crossing change” which is a local move on knot diagrams. This is a joint work with Akio Kawauchi and Kengo Kishimoto.