Spectral variation, normal matrices, and finsler geometry

Spectral Variation, Normal Matrices, and Finsler Geometry

Unicorns in Finsler Geometry

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

Relative volume comparison theorems in Finsler geometry and their applications

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

Spectral Variation Bounds for Diagonalisable Matrices

This note is related to an earlier paper by Bhatia, Davis, and Kittaneh 4]. For matrices similar to Hermitian, we prove an inequality complementary to the one proved in 4, Theorem 3]. We also disprove a conjecture made in 4] about the norm of a commutator.

The Geometry of Finsler Spaces

The term "Finsler space " evokes in most mathematicians the picture of an impenetrable forest whose entire vegetation consists of tensors. The purpose of the present lecture is to show that the association of tensors (or differential forms) with Finsler spaces is due to an historical accident, and that, at least at the present time, the fruitful and relevant problems lie in a different directio...