Scalar curvatures on $S\sp 2$

Scalar Curvatures of Hermitian Metrics on the Moduli Space of Riemann Surfaces

In this article we show that any finite cover of the moduli space of closed Riemann surfaces of g genus with g > 2 does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which is equivalent to the Teichmüller metric, on any finite cover of the moduli space is ...

A note on p-curvatures

In this note, we give an arithmetic criterion for the Lie-irreducibility of linear differential equations based on p-curvatures.

On the Non-uniqueness of Conformal Metrics with Prescribed Scalar and Mean Curvatures on Compact Manifolds with Boundary

For a compact Riemannian manifold (M, g) with boundary and dimension n, with n ≥ 2, we study the existence of metrics in the conformal class of g with scalar curvature Rg and mean curvature hg on the boundary. In this paper we find sufficient and necessary conditions for the existence of a smaller metric g̃ < g with curvatures Rg̃ = Rg and hg̃ = hg. Furthermore, we establish the uniqueness of such...

Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data

Curvatures of Sobolev Metrics on Diffeomorphism Groups

Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, while positive curvature suggests stability. In the first part of the paper we s...