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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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Quantum Confinement for the Curvature Laplacian −Δ + cK on 2D-Almost-Riemannian Manifolds
Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the Grushin plane. They are generalized Riemannian structures for...
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Analytic regularity for solutions to sums of squares: an assessment
We present a brief survey on the state of the theory of the real analytic regularity (real analytic hypoellipticity) for the solutions to sums of...
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Symplectic Geometry And Differential Equations
From the beginning symplectic geometry has been very intimately connected with first order differential equations. However, it is only during the...
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Sub-Riemannian Geometry and Hypoelliptic Operators
In this course we carefully define the notion of a non-holonomic manifold, which is a manifold with a certain non-integrable smooth sub-bundle of the...
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Geodesics in Geometry with Constraints and Applications
In this course we carefully define the notion of a non-holonomic manifold which is a manifold with a certain non-integrable distribution. We describe...
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First-Order Theory
Consider a nonholonomic system \(\dot{q}=\sum _{i=1}^{m}u_iX_i(q)\) , on a...
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Metrics with equatorial singularities on the sphere
Motivated by optimal control of affine systems stemming from mechanics, metrics on the two-sphere of revolution are considered; these metrics are...
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Ergodicity of Markov Semigroups with Hörmander Type Generators in Infinite Dimensions
We develop an effective strategy for proving strong ergodicity of (nonsymmetric) Markov semigroups associated to Hörmander type generators when the...
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Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie...
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Convexity and semiconvexity along vector fields
Given a family of vector fields we introduce a notion of convexity and of semiconvexity of a function along the trajectories of the fields and give...
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Regularity results for p-harmonic functions in higher order Grušin planes
We study the interior regularity for nondegenerate p -harmonic functions in Grušin planes of higher order. The local boundedness of the horizontal...
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On the Regularity of Nonlinear Subelliptic Equations
We prove C⧜ regularity results for Lipschitz solutions of nondegenerate quasilinear subelliptic equations of p-Laplacian type for a class of...
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Nonlinear subelliptic equations
In this paper, we study the higher order regularity for weak solutions of a class of quasilinear subelliptic equations. We introduce the notion of ν -c...
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Limiting behavior of solutions of subelliptic heat equations
We investigate the behavior, as ε → 0 + , of ε log w ε ( t, x ) where w ε are solutions of a suitable family of subelliptic heat equations. Using the...
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Subelliptic Cordes Estimates in the Grušin Plane
We apply subelliptic Cordes conditions and Talenti–Pucci type inequalities to prove W 2,2 and C 1,α estimates for p -harmonic functions in the Grušin...
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Fine Properties of Sets of Finite Perimeter in Doubling Metric Measure Spaces
The aim of this paper is to study the properties of the perimeter measure in the quite general setting of metric measure spaces. In particular,...