News
Welcome (again!) to the Finsler Geometry Newsletter.
The original aim of the Newsletter was to promote the interaction
between researchers in convex, integral, metric, and symplectic geometry
by providing them with a quick, accessible medium for communicating ideas,
announcements, examples, counterexamples, and remarks. However, at the time
I started this site wikis and blogs were not so common as they are now and the
primitive infrastructure I designed was never up to my expectations. In order
to take advantage of the new technology, the Newsletter will move in the next few
months, but during that time this site will be maintained and updated.
Thanks to my colleagues at Poly for hosting this site !
Criticisms and comments should be addressed to the
The webmaster:
Juan Carlos Alvarez
New postings
Three papers on Hilbert geometries
Three papers on systolic inequalities

About Finsler Geometry
Finsler manifolds, manifolds whose tangent spaces carry a norm that
varies smoothly with the base point, were born prematurely in 1854
together with the Riemannian counterparts in Riemann's groundbreaking
Habilitationsvortrag. I say prematurely because in
1854 Minkowski's work on normed spaces and convex bodies was still
forty three years away, and thus not even the infinitesimal geometry
on which Finsler manifolds are based was understood at the time.
Apparently, Riemann did not know what to make of these 'more general
class' of manifolds whose element of arclength does not originate
from a scalar product and, fatefully, put in a bad word for them:
Investigation of this more general class would actually require no
essential different principles, but it would be rather timeconsuming
and throw relatively little new light on the study of Space, especially
since the results cannot be expressed geometrically
Given the awe in which we rightfully regard Riemann's achievements
and uncanny geometrical intuition, it is tempting to take the above
quotation out of historical context and to dismiss Finsler geometry
altogether. But, if we think of the great advances in convex geometry,
the calculus of variations, integral geometry, the theory of metric
spaces, and symplectic geometry that have taken place since 1854, then
we may be moved to reassess Riemann's statement and to consider applying
these new tools to develop the subject in a way that Riemann could not
have foreseen.
J.C. Alvarez Paiva, Some problems on Finsler
geometry
