相关论文: Monge surfaces and planar geodesic foliations
We consider compact connected minimal surfaces, with a pair of boundary curves (not necessarily convex) in distinct planes, that have least-area amongst all orientable surfaces with the same boundary. When the planes containing these two…
We develop the concept of integral Menger curvature for a large class of nonsmooth surfaces. We prove uniform Ahlfors regularity and a $C^{1,\lambda}$-a-priori bound for surfaces for which this functional is finite. In fact, it turns out…
We construct a new family of simply connected minimal complex surfaces with $p_g=1$, $q=0$, and $K^2=8$ using a $\mathbb{Q}$-Gorenstein smoothing theory.
Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of 3-dimensional space-forms. This papers considers more…
It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to…
In this paper we study surfaces foliated by a uniparametric family of circles in the homogeneous space Sol$_3$. We prove that there do not exist such surfaces with zero mean curvature or with zero Gaussian curvature. We extend this study…
A periodic surface is one that is invariant by a 2D lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching…
We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…
We completely describe the Fano scheme of lines for a projective toric surface in terms of the geometry of the corresponding lattice polygon.
Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual…
A two dimensional surface can be considered as three dimensional shell whose thickness is negligible in comparison with the dimension of the whole system. The quantum mechanics on surface can be first formulated in the bulk and the limit of…
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…
Moir\'e patterns, typically formed by overlaying two layers of two-dimensional materials, exhibit an effective long-range periodicity that depends on the short-range periodicity of each layer and their spatial misalignment. Here, we study…
We use computer simulations and simple theoretical models to analyze the morphologies that result when rod-like particles end-attach onto a curved surface, creating a finite-thickness monolayer aligned with the surface normal. This geometry…
We present a few general results on foliations of 4-manifolds by surfaces: existence, tautness, relations to minimal genus of embedded surfaces; as well as some open problems. We hope to stimulate interest in this area.
Surfaces admitting flows all whose orbits are dense are called minimal. Minimal orientable surfaces were characterized by J.C. Beni\`{e}re in 1998, leaving open the nonorientable case. This paper fills this gap providing a characterization…
Dilation surfaces are geometric surfaces modelled after the complex plane whose structure group is generated by the groups of translations and dilations. For any dilation surface, for any direction $\theta$ in $S^1$, there exists a…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions are…
To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a…