Related papers: Developments around positive sectional curvature

This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…

This survey is an invitation to recent developments in higher dimensional birational geometry.

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…

A brief history, the current state, and future directions of spin mechanics are presented.

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…

This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.

We review all the cosmic shear results obtained so far, with a critical discussion of the present strengths and weaknesses. We discuss the future prospects and the role cosmic shear could play in a precision cosmology era.

We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…

We present a brief review of some recent results on conformal anomalies in four and more dimensions. The discussion is intended for relativists, so some background on the quantum origin of anomalies and of their simple properties in D=2 is…

We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.

We briefly review some of the recent developments in QCD spin physics.

We consider the geometric evolution of a network in the plane, flowing by anisotropic curvature. We discuss local existence of a classical solution in the presence of several smooth anisotropies. Next, we discuss some aspects of the…

In this article we discuss the effect of curvature on dynamics when a physical system moves adiabatically in a curved space. These effects give a way to measure the curvature of the space intrinsically without referring to higher…

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…

Studies of galaxy evolution at optical and near-infrared wavelengths have reached an interesting point in their historical development and the arrival of a new millenium provides an appropriate occasion to review the overall direction in…

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is…

For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…

In this article a sequential theory in the category of spaces and proper maps is described and developed. As a natural extension a sequential theory for exterior spaces and maps is obtained.

The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…