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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,051 papers · 148 categories

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4 results for “nilpotentization”
On G2\mathrm{G}_2 and Sub-Riemannian Model Spaces of Step and Rank Threemath.DG

Complete classification of sub-Riemannian spaces with step and rank three.

problem Classifying sub-Riemannian model spaces with specific step and rank.
method Complete classification based on nilpotentization and algebra realization.
result No nontrivial sub-Riemannian model spaces of step and rank three with free nilpotentization.
sub-Riemannian model spacesstep and rank threenilpotentizationisometry algebrasexceptional Lie algebra g2
2019-01-20abs ↗pdf ↗
Carnot rectifiability of sub-Riemannian manifolds with constant tangentmath.MG

Rectifiability shown for sub-Riemannian manifolds with Carnot tangent structure.

problem Understanding rectifiability in sub-Riemannian manifolds with specific tangent properties.
method Analyzing nilpotentization and embedding properties of sub-Riemannian manifolds into Carnot groups.
result Sub-Riemannian manifolds are countably rectifiable under certain conditions.
rectifiabilitysub-Riemannian manifoldsCarnot groupsnilpotentizationembedding
2019-01-31abs ↗pdf ↗
Spectral asymptotics for sub-Riemannian Laplaciansmath.DG

Study spectral properties of sub-Riemannian Laplacians, proving quantum ergodicity and heat kernel asymptotics.

problem Spectral properties of sub-Riemannian Laplacians.
method Quantum ergodicity results, small-time asymptotics of sub-Riemannian heat kernels, Weyl law.
result Weyl law and spectral concentration on Lie brackets of length r-1.
sub-Riemannian Laplaciansspectral propertiesquantum ergodicityheat kernelsWeyl law
2022-12-06abs ↗pdf ↗