Related papers: Multiple Solutions to the Planar Plateau Problem
Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets…
We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.
We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface $\Sigma$ admitting conical singularities of orders $\alpha_i$'s at points $p_i$'s. In particular, we are concerned with the case…
An examples of solutions of nonlinear differential equations associated with developable, ruled and minimal surfaces are constructed.
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the…
We give obstructions - in terms of Gaussian maps - for a marked Prym curve $(C,\alpha,T_d)$ to admit a singular model lying on an Enriques surface with only one $d$-ordinary point singularity and in such a way that $T_d$ corresponds to the…
Following on from ``Hyperbolic Plateau problems'' (by the same author), we provide a complete geometric description of solutions to the Plateau problem $(S,\phi)$ when $S$ is a compact Riemann surface with a finite number of points removed.
We show that geodesics in the upper half-plane attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf{Q}}$ are the only irreducible algebraic curves whose image via the $j$-invariant is contained in an algebraic…
The mixed scalar curvature is one of the simplest curvature invariants of a foliated Riemannian manifold. We explore the problem of prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the…
We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in $\mathbb{R}^{3}$, and whose…
A number of boundary problems in multidimensional elasticity theory are solved. The solutions can be treated as the simplest cosmological models. Some specific properties of the solutions and experimental consequences of the theory are…
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…
In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce…
The radial limits of a nonparametric prescribed mean curvature surface uniquely determine the surface.
The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the…
We provide a very effective and explicit algorithm of finding a Puiseux expansion of a cuspidal singularity of a plane curve, when this singularity is given in a parametric form.
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodicity of that surface is also discussed.
In this paper, we propose a resolvent of an equilibrium problem in a geodesic space with negative curvature having the convex hull finite property. We prove its well-definedness as a single-valued mapping whose domain is whole space, and…