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Surface measure on, and the local geometry of, sub-Riemannian manifolds
We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we...
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Second Variation of Sub-Riemannian Surface Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups
We establish the second variation of sub-Riemannian surface measure for minimal non-horizontal submanifolds of a sub-Riemannian stratified Lie group....
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Pseudocomplete Riemannian Analytic Manifolds
AbstractWe study the analytic extension of a locally given Riemannian analytic metric to a metric of a nonextendable manifold. Various classes of...
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Minimal graphs in Riemannian spaces
In this treatise, we discuss existence and uniqueness questions for parametric minimal surfaces in Riemannian spaces, which represent minimal graphs....
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Riemannian Surfaces with Simple Singularities
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends...
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Catenaries in Riemannian surfaces
The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author (López,
ar**v:2208.13694 ...
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Ruled Surfaces in 3-Dimensional Riemannian Manifolds
In this work, ruled surfaces in 3-dimensional Riemannian manifolds are studied. We determine the expressions for the extrinsic and sectional...
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Efficient Random Walks on Riemannian Manifolds
According to a version of Donsker’s theorem, geodesic random walks on Riemannian manifolds converge to the respective Brownian motion. From a...
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The Geometry of Riemannian Curvature Radii
We study the geometric structures associated with curvature radii of curves with values on a Riemannian manifold ( M , g ). We show the existence of...
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Riemannian Manifolds
A Riemannian manifold M n is a smooth manifold equipped with an inner product (Riemannian metric) g(X, Y ) in the tangent space at each point;...
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On the index of a free-boundary minimal surface in Riemannian Schwarzschild-AdS
We consider the index of a certain non-compact free-boundary minimal surface with boundary on the rotationally symmetric minimal sphere in the...
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Modulus Inequalities on Riemannian Surfaces
In this chapter, we study non-homeomorphic map**s of Riemannian surfaces of the Sobolev class. We have established estimates for the distortion of...
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Restricted Mean Value Property on Riemannian manifolds
A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been...
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Generalization of the Notion of Completeness of a Riemannian Analytic Manifold
In this paper, we discuss the concept of an analytic prolongation of a local Riemannian metric. We propose a generalization of the notion of...
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Biharmonic Riemannian Submersions from a 3-Dimensional BCV Space
BCV spaces are a family of 3-dimensional Riemannian manifolds which include six of Thurston’s eight geometries. In this paper, we give a complete...
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Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact...
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A Riemannian Point of View for a Quadrature Surface Free Boundary Problem
The aim of this work is to propose a Riemannian point of view of a free boundary problem that is equivalent to a quadrature surface problem. Our...
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Homogeneous Riemannian structures in dimension three
In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a non-symmetric...
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Front Asymptotics of a Flat Sub-Riemannian Structure on the Engel Distribution
AbstractWe approximate the front of a flat sub-Riemannian structure on the Engel distribution in a neighborhood of a non-subanalytic singularity by...
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Pseudo-parallel Lorentzian Surfaces in Pseudo-Riemannian Space Forms
In this work, we give a characterization of pseudo-parallel Lorentzian surfaces with non-flat normal bundle in pseudo-Riemannian space forms as
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