Generic metrics make geodesic nets dense.
problem Density of geodesic nets under generic metrics.
method Proving density for Baire-generic metrics.
result Union of geodesic nets images is dense.
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5 results for “Baire-generic”
Theorem shows generic metrics yield non-degenerate geodesic nets.
problem Characterizing geodesic nets on generic metrics.
method Proving all connected embedded nets are non-degenerate for Baire-generic metrics.
result All stationary geodesic nets are non-degenerate for generic metrics.
Generic geodesic nets are dense in high-dimensional manifolds.
problem Density of non-closed geodesic nets in high-dimensional manifolds.
method Proving density for a generic metric on a manifold.
result Stationary geodesic nets that are not closed geodesics form a dense set.
Improved Kuznecov remainder estimates for generic metrics.
problem Estimating period integrals of Laplace eigenfunctions on manifolds.
method Two-term asymptotic expansion and elimination of oscillatory second term.
result Improved remainder estimates for Baire-generic metrics.
The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.
problem Understanding the behavior of waves on Kerr-AdS black holes.
method Analyzing linear scalar perturbations and studying poles of the interior scattering operator.
result Perturbations blow up at the Cauchy horizon under certain non-Diophantine conditions.