There exists a nonrecursive c.e. set A such that for every X ≡_m A there is a c.e. B ≡_m A with X ≰_fo B, so the m-degree of A contains no least finite-one degree.
On the geometry and dynamics of diffeomorphisms of surfaces
8 Pith papers cite this work. Polarity classification is still indexing.
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The model on the Lorentzian cone with algebraic operators reproduces the standard hydrogen atom energy spectrum and wavefunction solutions in a Schwartz subspace.
Establishes interior Hölder gradient estimates, pointwise improvements, and Schauder-type estimates at extremal points for viscosity solutions of degenerate fully nonlinear elliptic PDEs with variable exponents p(x) and q(x).
Moduli stacks for diagrams of λ-connections are constructed and proven algebraic when the base is a smooth projective scheme over an algebraically closed field of characteristic zero.
Proves infinitely many periodic points for asymptotically linear non-degenerate Hamiltonian diffeomorphisms on R^{2n} that are unitary at infinity, decay quickly to their linear part, and obey a twist condition.
Proves unimodality of rank polynomials for loop fence posets and tagged arcs arising from cluster algebras on surfaces, plus almost interlacing symmetry and a log-concavity conjecture for single-curve laminations.
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
citing papers explorer
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A computably enumerable many-one degree with no least finite-one degree
There exists a nonrecursive c.e. set A such that for every X ≡_m A there is a c.e. B ≡_m A with X ≰_fo B, so the m-degree of A contains no least finite-one degree.
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A new model for the quantum mechanics of the Hydrogen atom
The model on the Lorentzian cone with algebraic operators reproduces the standard hydrogen atom energy spectrum and wavefunction solutions in a Schwartz subspace.
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Gradient Regularity for Fully Nonlinear Equations with Variable Degeneracy and Hamiltonian Lower-Order Terms
Establishes interior Hölder gradient estimates, pointwise improvements, and Schauder-type estimates at extremal points for viscosity solutions of degenerate fully nonlinear elliptic PDEs with variable exponents p(x) and q(x).
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Moduli stacks of quiver connections and non-Abelian Hodge theory
Moduli stacks for diagrams of λ-connections are constructed and proven algebraic when the base is a smooth projective scheme over an algebraically closed field of characteristic zero.
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A Poincar\'e-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
Proves infinitely many periodic points for asymptotically linear non-degenerate Hamiltonian diffeomorphisms on R^{2n} that are unitary at infinity, decay quickly to their linear part, and obey a twist condition.
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Unimodality and Cluster Algebras from Surfaces
Proves unimodality of rank polynomials for loop fence posets and tagged arcs arising from cluster algebras on surfaces, plus almost interlacing symmetry and a log-concavity conjecture for single-curve laminations.
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Minimal surfaces with closed curvature lines
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
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General Relativity via differential forms -- explorations in Plebanski's Formalism for GR
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.