Some remarks on Huisken's monotonicity formula for mean curvature flow

We discuss a monotone quantity related to Huisken's monotonicity formula and some technical consequences for mean curvature flow.Comment: in "Singularities in nonlinear evolution phenomena and applications", 157-169, CRM Series, 9, Ed. Sc. Norm. Pisa, 200

Evolution of the Weyl Tensor under the Ricci Flow

We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons

A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport

We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non-smooth metric measure spaces with Ricci curvature bounded from below

Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds

The paper is concerned with the properties of the distance function from a closed subset of a Riemannian manifold, with particular attention to the set of singularities

Line profile analysis of the Delta Scuti star HD2724=BB Phe: mode identification and amplitude variations

The line profile variations of the Delta Scuti star HD 2724=BB Phe were studied on the basis of new 189 high-resolution spectrograms covering 52 hours of observations on a baseline of 8.3 days. By combining these results with those of a previous campaign 13 pulsation modes were identified: 5 of them are both photometric and spectroscopic, 3 are purely spectroscopic and 5 purely photometric. For the first time it was possible to compare spectroscopic data taken in two different seasons: 6 modes were found to be common to both datasets and furthermore strong amplitude variations of the excited modes were detected. The fit of the line profile variations with a model of non-radial pulsating star allowed us to obtain a reasonable estimate of the inclination of the rotational axis and to propose the l,m typing of the spectroscopic modes. The frequency content resembles that of 4 CVn, a delta Sct star with similar physical parameters.Comment: 7 pages (in A&A style), 5 ps figures (Fig. 4 in colour) Accepted for A&A Main Journa

Motion by curvature of networks with two triple junctions

We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution