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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.

168,657 papers · 148 categories

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← all fields·3 papers on “scalar curvature” in Differential Geometry · 1 week

Positivity and non-positivity results for the sixth-order

Q

-curvature of conformal metrics in

\mathbb{R}^n

math.DG

For certain metrics, the paper finds that the sixth-order Q-curvature is positive in some dimensions but negative in others.

problem Analyzing the positivity and non-positivity of the sixth-order Q-curvature for conformal metrics.

method Examining specific conditions on scalar curvature and Q-curvature, constructing examples to demonstrate the behavior of the sixth-order Q-curvature.

result The sixth-order Q-curvature can be positive in some dimensions but negative in others, depending on the metric.

Q-curvature conformal metrics scalar curvature positive results negative results

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 ↗

Scalar Curvature and Product Manifoldsmath.DG

4D manifolds without positive scalar curvature but products do.

problem Existence of positive scalar curvature on manifolds and products.

method Counterexamples and product constructions.

result Found 4D manifolds without positive scalar curvature but products do.

Scalar curvature Product manifolds Counterexamples Rosenberg's conjecture

2026-07-15abs ↗pdf ↗