곡면이 동그랗기 위한 충분조건은 적어도 14가지가 있다.
이 강연에서는 이들 중에서 평균곡률(mean curvature)을 이용한 충분조건에 관하여 옛 결과와 최근 결과를 알아볼 예정이다.

In this talk, we are going to discuss  the homogenization process on self-organizing materials or information, and to find out the effective (or averaged) partial differential equations describing the first order approximation through filtering out the small oscillations occurred by inhomogeneous distribution of materials or information. One simple example is when two conductors with different conductivity distributed periodically on the plane with small periodicity. One of the interesting questions is what is the averaged effective conductivity. We are going to discuss Viscosity Method developed recently and to compare it with well known Energy method.

A rendezvous number for a metric space M is a number a such that, for every finite subset Q of M, there is an element p in M, such that the average distance from p to the elements in Q is a.

O. Gross showed in 1964 that every compact connected metric space has precisely one rendezvous number. This result is a consequence of von Neumann’s min-max theorem in game theory.

In an article in the American Math. Monthly 93(1986) 260-275, J. Cleary and A. A. Morris asked if a (more) elementary proof of Gross’ result exists.

In this talk I shall formulate a min-max result for real matrices which immediately implies these results of Gross and von Neumann.

The proof is easy and involves only mathematical induction.