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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.

169,341 papers · 148 categories

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4 results for “two-systole”
On the two-systole of real projective spacesmath.DG

Characterizes the largest two-systole in real projective spaces.

problem Finding the largest two-systole in real projective spaces.
method Integral-geometric formula for minimal two-spheres, characterizing metrics with largest two-systole.
result Each homogeneous metric on the three-dimensional real projective space is the unique metric with the largest possible two-systole among metrics with the same volume.
two-systolereal projective spacehomogeneous metricintegral-geometric formula
2018-09-10abs ↗pdf ↗
Balanced metrics, Zoll deformations and isosystolic inequalities in CPn\mathbb{C}P^nmath.DG

The paper analyzes systoles of complex projective spaces under various metrics.

problem Behavior of systoles in complex projective spaces for different metrics.
method Integral geometric techniques and careful analysis of systole functional.
result Balanced metrics locally minimize the systole on volume-normalized metrics.
systolecomplex projective spacehomogeneous metricsbalanced metricsZoll deformations
2023-10-16abs ↗pdf ↗