Conjectures that simple geodesics on finite covers of the modular orbifold have rational, quadratic, or transcendental endpoints, with proofs for minimal geodesic laminations and the modular torus cover.
An introduction to contact topology , volume =
4 Pith papers cite this work. Polarity classification is still indexing.
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A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
CR Paneitz operator on non-embeddable 3D tori has infinitely many negative eigenvalues under mild assumptions.
Derives an obstruction formula for Poisson and Jacobi structures induced by 2-covariant tensors and recovers the classical brackets in symplectic, locally conformally symplectic, cosymplectic, and contact geometries.
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Transcendence of simple geodesics on finite modular covers
Conjectures that simple geodesics on finite covers of the modular orbifold have rational, quadratic, or transcendental endpoints, with proofs for minimal geodesic laminations and the modular torus cover.