Related papers: (Weak) $m$-extremals and $m$-geodesics

We consider the set of extremal points of the generalized unit ball induced by gradient total variation seminorms for vector-valued functions on bounded Euclidean domains. These are central to the understanding of sparse solutions and…

Let (X,L) be a polarized compact manifold, i.e. L is an ample line bundle over X and denote by H the infinite dimensional space of all positively curved Hermitian metrics on L equipped with the Mabuchi metric. In this short note we show,…

We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…

In this article, the authors prove the existence of global weak solutions to the inviscid three-dimensional quasi-geostrophic equation. This equation models the evolution of the temperature on the surface of the earth. It is widely used in…

In this paper we exhibit a similarity between Euclidean Ramsey problems and Knaster-type problems. By borrowing ideas from Ramsey theory we prove weak Knaster properties of non-equatorial triangles in spheres, and of simplices in Euclidean…

We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous…

Starting from pointwise gradient estimates for the heat semigroup, we study three characterizations of weak lower curvature bounds on metric graphs. More precisely, we prove the equivalence between a weak notion of the Bakry-\'Emery…

Suppose (X,\omega) is a compact K\"ahler manifold. In the present work we propose a simple construction for weak geodesic rays in the space of K\"ahler metrics that seems to be tied together with properties of the class E(X,\omega). As an…

We deal with a robust notion of weak normals for a wide class of irregular curves defined in Euclidean spaces of high dimension. Concerning polygonal curves, the discrete normals are built up through a Gram-Schmidt procedure applied to…

In this paper we provide mixed weak type inequalities generalizing previous results in an earlier work by Caldarelli and the second author and also in the spirit of earlier results by Lorente, Martell, P\'erez and Riveros. One of the main…

We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…

We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…

In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special…

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.

We prove a general fusion theorem for complete orientable minimal surfaces in $\mathbb{R}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are…

We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries…

In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

We give a definition of weak geodesics on prox-regular subsets of Riemannian manifolds as continuous curves with some weak regularities. Then obtaining a suitable Lipschitz constant of the projection map, we characterize weak geodesics on a…