Date: July 1, 2004

Venue: Room 4-508, Department of Mathematics, Hokkaido University

Organizer: TONEGAWA Yoshihiro (Hokkaido Univ.), FURUHATA Hitoshi (Hokkaido Univ.)

http://www.math.sci.hokudai.ac.jp/

http://coe.math.sci.hokudai.ac.jp/

Program:

10:00- MAEDA Yoshiaki (Keio Univ.)

Local isometric embeddings of Riemannian manifolds of dimension two and three (1)

13:30- NAKAMURA Gen (Hokkaido Univ.)

Local isometric embeddings of Riemannian manifolds of dimension two and three (2)

15:30- HAN Qing (Univ. of Notre Dame)

Isometric embedding surfaces in R^3

Abstract: Can we always isometrically embed any surface (a 2-dim Riemannian manifold) in R^3? This is a long standing problem in differential geometry. The obstruction comes from the sign of the Gauss curvature. There are two aspects of this problem, global isometric embedding and local isometric embedding. The problem is reduced to solving Darboux equation, a fully nonlinear equation of the second order. The type of the Darboux equation is determined by Gauss curvature. In this talk, I shall first review Nirenberg's solution of Weyl problem and Lin's results on local isometric embedding. Then I shall present some new results concerning the local isometric embedding if Guass curvature is nonpositive or Guass curvature changes its sign.

The lecture by AGAOKA is canceled.

Other Workshops:

[July 21] Workshop on Affine Immersions and Information

[August 4-6] The 29th Sapporo Symposium on Partial Differential Equations

[TONEGAWA] [FURUHATA]