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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.

168,742 papers · 148 categories

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← all fields·4 papers on “rigidity” in Differential Geometry · 1 week

Rigidity of weak solutions for anisotropic N-Laplacian equation with Neumann or Robin boundary conditionmath.AP

Paper proves rigidity of weak solutions for anisotropic N-Laplacian equations with Neumann or Robin boundary conditions.

problem Rigidity of weak solutions for anisotropic N-Laplacian equations with boundary conditions.

method Established a key integral inequality involving anisotropic gradient and second fundamental form, proving rigidity under natural monotonicity assumptions.

result All weak solutions to Neumann boundary problems are constant without a priori boundedness assumption.

rigidity weak solutions anisotropic N-Laplacian Neumann boundary Robin boundary

2026-07-23abs ↗pdf ↗

The Liouville equation on Riemannian surfaces: the role of volume growth in classification and rigidity resultsmath.AP

Study Liouville equation on Riemannian surfaces, linking volume growth to classification results.

problem Classifying solutions and manifolds of the Liouville equation on Riemannian surfaces.

method Analyzing the Liouville equation

-Δu = e^u

on Riemannian surfaces with non-negative Ricci curvature, considering asymptotic volume growth.

result Established classification results for solutions and manifolds, revealing a connection between volume growth and classification.

Liouville equation Riemannian surfaces volume growth classification rigidity

2026-07-22abs ↗pdf ↗

Sharp Weitzenböck and PIC2 Estimates from Sectional-Scalar Curvature Pinchingmath.DG

Sharp estimates link curvature to topology, proving manifold rigidity.

problem Proving rigidity of manifolds under curvature pinching conditions.

method Sharp pointwise estimates and normalized Ricci flow.

result Proves manifold rigidity under strict sectional-scalar curvature pinching.

curvature pinching topology rigidity normalized Ricci flow algebraic curvature tensor

2026-07-20abs ↗pdf ↗

Rigidity of positive mass theorem with fast metric decaymath.DG

New findings on flatness of certain metrics with fast decay.

problem Rigidity of positive mass theorem under fast metric decay.

method Considered metrics with nonnegative scalar curvature and rapid decay at infinity.

result Any such metric is necessarily flat in dimensions 4 and higher if decay rate exceeds Schwarzschild metric.

positive mass theorem rigidity Euclidean space scalar curvature metric decay

2026-07-19abs ↗pdf ↗