Related papers: Developments around positive sectional curvature

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.

This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.

In this chapter, we survey some recent developments in the field of geophysical inversion. We aim to provide an accessible general introduction to the breadth of current research, rather than focussing in depth on particular topics. In…

This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.

This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.

The article contains a brief description on the study of conformal scalar curvature equations, and discusses selected topics and questions concerning the equations in open spaces.

In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

In this short note we discuss some recent results about two-positive Ricci curvature and their applications to positive Einstein curvature.

Recent data suggest that the Universe could be positively curved. Combined with an inflationary stage, this might lead to a curvature bounce instead of the Big Bang. The background evolution is presented, as a function of the parameters…

We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media…

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…

This article serves as an introduction to the special volume on Positive Geometry in the journal Le Matematiche. We attempt to answer the question in the title by describing the origins and objects of positive geometry at this early stage…

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

Surveys of the local and distant Universe are the means to test and improve our models of galaxy formation. Substantial successes in the models are evident, while there is also considerable recent progress in identifying what remains to be…

The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.

In this paper, we study the interplay of geometry and positive scalar curvature on a complete, non-compact manifold with non-negative Ricci curvature. In three-dimensional manifold, we prove a minimal volume growth, an estimate of integral…

This is a survey written for a special edition of the journal of differential geometry.