3 citations · 3 across the 9 of their papers we have counts for
10 papers
Singular Sets of Riemannian Exponential Maps in Hydrodynamics
James Benn, Patrick Heslin, Leandro Lichtenfelz +1
We prove that the singular sets for the Lagrangian solution maps of the two-dimensional inviscid Euler and generalized surface quasi-geostrophic equations are Gaussian null sets. T…
Ricci curvature for hydrodynamics on the sphere
Leandro Lichtenfelz, Klas Modin, Stephen C. Preston
The geometric description of incompressible hydrodynamics, as geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms, enables notions of curvature i…
Homotopy Type of the Space of Fibrations of the Three-sphere by Simple Closed Curves
Dennis Deturck, Ziqi Fang, Herman Gluck +4
We show that the moduli space of all smooth fibrations of a three-sphere by simple closed curves has the homotopy type of a disjoint union of a pair of two-spheres if the fibers ar…
Conjugate points on Lie groups with left-invariant metrics
Alice Le Brigant, Leandro Lichtenfelz, Stephen C. Preston
We prove sufficient conditions for the existence of conjugate points along geodesics of a left-invariant metric on a Lie group, using a reformulation of the index form in terms of…
Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid
Leandro Lichtenfelz, Taito Tauchi, Tsuyoshi Yoneda
The existence of a conjugate point on the volume-preserving diffeomorphism group of a compact Riemannian manifold M is related to the Lagrangian stability of a solution of the inco…
Deformation retraction of the group of strict contactomorphisms of the three-sphere to the unitary group
Dennis DeTurck, Herman Gluck, Leandro Lichtenfelz +3
We prove that the group of strict contactomorphisms of the standard tight contact structure on the three-sphere deformation retracts to its unitary subgroup U(2).
Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds
Leandro Lichtenfelz, Gerard Misiolek, Stephen C. Preston
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fre…
A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundary
Leandro Lichtenfelz, Tsuyoshi Yoneda
Using numerical simulations of the axisymmetric Navier-Stokes equations with swirl on a no-slip flat boundary, Hsu-Notsu-Yoneda [J. Fluid Mech. 2016] observed the creation of a hig…
Nonuniqueness of solutions of the Navier-Stokes equations on negatively curved Riemannian manifolds
Leandro Lichtenfelz
In a well-known work, M. Anderson constructed a Hadamard manifold which carries non-zero harmonic -forms when , thus disproving the Dodziuk-Singer c…
Almost isometries of non-reversible metrics with applications to stationary spacetimes
Miguel Angel Javaloyes, Leandro Lichtenfelz, Paolo Piccione
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particu…