While the general impression is that Finsler geometry is a complicated
and computation-intensive field, the reality is that, like
convex, metric, and integral geometry, many of its examples and constructions
are natural, elementary, and non-trivial. No doubt this assertion will come
as a surprise to some and therefore I will back it up with a link to a paper
on Hilbert's fourth problem that I wrote for advanced undergraduates and
beginning graduate students. The paper is based on (part of) a talk I gave
at the MASS Colloquium --- a wonderful program where talented undergraduate
students from all over the United States converge to Penn State for a semester
of advanced mathematics --- and will appear in its proceedings.
I have not signed away my copyright I invite other researchers in Finsler and Minkowski geometry to write this sort of expository papers in order to motivate graduate and undergraduate students to learn about Finsler and Minkowski spaces. I would be happy to post their preprints here.
For the Finsler geometer, I mention that hidden in exercise 6.3
is the following (new?) result:
14th of October, 2002. |
This is a survey on Radon curves and the relationship between circles and solutions of the isoperimetric problem in two-dimensional normed spaces. |