相关论文: Smoothness of collapsed regions in a capillarity m…

We study the descent behaviour of homotopy-theoretic properties of smooth complex affine surfaces under finite surjective morphisms. We first examine the Eilenberg-MacLane property and show, by means of an explicit counterexample, that it…

We consider a functional related with phase transition models in the Heisenberg group framework. We prove that level sets of local minimizers satisfy some density estimates, that is, they behave as "codimension one" sets. We thus deduce a…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…

We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.

The volume hypothesis suggests deep learning is effective because it is likely to find flat minima due to their large volumes, and flat minima generalize well. This picture does not explain the role of large datasets in generalization.…

Establishing the convergence of splines can be cast as a variational problem which is amenable to a $\Gamma$-convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, $n$, as…

Let $(M,\bar{g}, e^{-f}d\mu)$ be a complete metric measure space with Bakry-\'Emery Ricci curvature bounded below by a positive constant. We prove that, in $M$, there is no complete two-sided $L_f$-stable immersed $f$-minimal hypersurface…

Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…

A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also…

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction…

Given a video and a set of input object masks, an omnimatte method aims to decompose the video into semantically meaningful layers containing individual objects along with their associated effects, such as shadows and reflections. Existing…

In this paper we prove that a capillary minimal surface outside the unit ball in $\mathbb {R}^3$ with one embedded end and finite total curvature must be either part of the plane or part of the catenoid. We also prove that a capillary…

We establish a generic vanishing theorem for surfaces in characteristic $p$ that lift to $W_2(k)$ and use it for surface classification of surfaces of general type with Euler characteristic 1 and large Albanese dimension.

We consider the Landau-de Gennes variational model for nematic liquid crystals, in three-dimensional domains. More precisely, we study the asymptotic behaviour of minimizers as the elastic constant tends to zero, under the assumption that…

Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincar\'e duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology…

In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…

We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…

Alexandrov's soap bubble theorem asserts that spheres are the only connected closed embedded hypersurfaces in the Euclidean space with constant mean curvature. The theorem can be extended to space forms and it holds for more general…

By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the…