相关论文: Minimal laminations with prescribed convex curvatu…
We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis,…
We use elementary methods to construct a minimal lamination of the interior of a positive cone in R3.
Given a compact closed subset $M$ of a line segment in $\mathbb{R}^3$, we construct a sequence of minimal surfaces $\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly to a limit lamination of $C$ away from…
We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and hence, finite) set of points on…
We study finite-energy blow-ups for prescribed Morse scalar curvatures in both the subcritical and the critical regime. After general considerations on Palais-Smale sequences we determine precise blow up rates for subcritical solutions: in…
For any prescribed closed subset of a line segment in Euclidean 3-space, we construct a sequence of minimal disks that are properly embedded in an open solid cylinder around the segment and that have curvatures blowing up precisely at the…
We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove…
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some…
We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…
In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in $\mathbb R^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries…
In this paper we prove a local removable singularity theorem for certain minimal laminations with isolated singularities in a Riemannian three-manifold. This removable singularity theorem is the key result used in our proof that a complete,…
Any sequence of properly embedded minimal disks in an open subset U of Euclidean 3-space has a subsequence such that the curvatures blow up on a relatively closed subset K of U and such that the disks converge in the complement of K to a…
This paper is devoted to the prescribed scalar curvature under minimal boundary mean curvature on the standard four dimensional half sphere. Using topological methods from the theory of critical points at infinity, we prove some existence…
This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation,…
We consider one of the generic regimes of formation of singularities. We obtain a detailed description of a possibly small, but fixed, neighborhood of the blowup point, up to (and including) the blowup time, and find that it is mean convex.…
In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the…
In this paper, we investigate the problem of prescribing Webster scalar curvatures on compact pseudo-Hermitian manifolds. In terms of the method of upper and lower solutions and the perturbation theory of self-adjoint operators, we can…
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for…
Milnor divides all bounded hyperbolic components of cubic polynomials into 4 types (A), (B), (C) and (D). In this article, we characterize the real laminations of cubic polynomials on the tame boundary of all bounded hyperbolic components…