相关论文: Korn inequalities for shells with zero Gaussian cu…

For singular corank 1 surfaces in $\mathbb R^3$ we introduce a distinguished normal vector called the axial vector. Using this vector and the curvature parabola we define a new type of curvature called the axial curvature, which generalizes…

Let M be a closed minimal hypersurface in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature. We prove that, if the sum of the cubes of all principal curvatures and the number of distinct principal curvatures are…

We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2\pi$, the main result being sufficient conditions for a positive function of class…

We study closed orientable surfaces satisfying the spectral condition $\lambda_1(-\Delta+\beta K)\geq\lambda\geq0$, where $\beta$ is a positive constant and $K$ is the Gauss curvature. This condition naturally arises for stable minimal…

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of…

This work concerns stability and instability of Einstein warped products with an Einsteinian fiber of codimension 1. We study the cases where the scalar curvature of the warped product and of the fiber are either both positive or both…

In this paper we examine numerically the properties, especially the scaling properties, of an isolated crescent singularity similar to that of a developable cone. The desired isolated crescent region is produced by applying six potential…

We study the deformation of a liquid interface with arbitrary principal curvatures by a flat circular sheet. Working first at small slopes, we determine the shape of the sheet analytically in the membrane limit, where the sheet is…

In this paper we derive, by two$-$scale convergence, periodically wrinked shell models starting from three dimensional linear elasticity, depending of the behaviour of the small parameter $\varepsilon>0$ and $p>1$, differents theories…

The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied {\it analytically}. To that end, we solve the Klein-Gordon wave equation for…

We give the first rigorous construction of complete, embedded self-shrinking hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The surfaces exist for any sufficiently large prescribed genus $g$, and are non-compact…

Using observations of cores to infer their intrinsic properties requires the solution of several poorly constrained inverse problems. Here we address one of these problems, namely to deduce from the projected aspect ratios of the cores in…

It is well known that there are two regimes in a standard one-dimensional Boolean percolation model: either the entire space is covered a.s., or the covered volume fraction is strictly less than one. The aim of this work is to demonstrate…

The isometric immersion of two-dimensional Riemannian manifolds or surfaces in the three-dimensional Euclidean space is a fundamental problem in differential geometry. When the Gauss curvature is negative, the isometric immersion problem is…

The Oleinik inequality for conservation laws and Aronson-Benilan type inequalities for porous medium or p-Laplacian equations are one-sided inequalities that provide the fundamental features of the solution such as the uniqueness and sharp…

Elastic curvature constants determine many structural and functional properties of fluid membranes. Methods to measure the mean curvature modulus have proved to be robust. In contrast, Gaussian curvature is an intrinsic property of a…

Significant progress has been made in understanding planetary core dynamics using numerical models of rotating convection (RC) in spherical shell geometry. However, the behaviour of forces in these models within various dynamic regimes of…

We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and…

We test the hypothesis that the starless cores may be gravitationally bound clouds supported largely by thermal pressure by comparing observed molecular line spectra to theoretical spectra produced by a simulation that includes…