Explicit constructions of closed even-dimensional manifolds with positive mixed sectional curvature on 1D totally geodesic circle foliations provide counterexamples to Toponogov's question by violating the predicted Ferus-Adams leaf dimension bound.
The fundamental equations of a submersion
4 Pith papers cite this work. Polarity classification is still indexing.
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The Extended Real Line with Reentry is the first compact path-connected US-not-KC space, obtained via a density-modified quotient of the extended reals.
Hydrodynamic limit of symmetric exclusion process on Poisson graphs approximating weighted Riemannian manifolds and principal bundles is a Fokker-Planck equation.
All computable increasing sequences converging to random reals converge at the same speed up to a constant factor, as this follows immediately from Bishop's upcrossing inequality.
citing papers explorer
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Closed counterexamples to Toponogov's question on mixed curvature
Explicit constructions of closed even-dimensional manifolds with positive mixed sectional curvature on 1D totally geodesic circle foliations provide counterexamples to Toponogov's question by violating the predicted Ferus-Adams leaf dimension bound.
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The Extended Real Line with Reentry: Separating US from KC in the Clontz Hierarchy
The Extended Real Line with Reentry is the first compact path-connected US-not-KC space, obtained via a density-modified quotient of the extended reals.
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Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles
Hydrodynamic limit of symmetric exclusion process on Poisson graphs approximating weighted Riemannian manifolds and principal bundles is a Fokker-Planck equation.
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Bishop's (up)crossing inequality and lower semicomputable random reals revisited
All computable increasing sequences converging to random reals converge at the same speed up to a constant factor, as this follows immediately from Bishop's upcrossing inequality.