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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·9 papers on “scalar curvature” in Differential Geometry · 1 month

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 ↗

Closed manifolds, model geometries, and volume related differentiable invariantsmath.DG

The study classifies manifolds based on their geometric properties and invariants.

problem Classifying manifolds based on their geometric and topological properties.

method Analyzing metrics through isometric embeddings and deformations, considering scalar curvature, Ricci tensor, and Einstein metrics.

result The KW type classification of manifolds and sigma invariant calculations.

manifolds geometry invariants isometric embeddings scalar curvature

2026-07-14abs ↗pdf ↗

Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifoldsmath.DG

Proves rigidity in product spaces using index theory.

problem Scalar curvature rigidity in product spaces.

method Fredholm family index theorem.

result Recover corresponding results of Clifford-linear index theory.

scalar curvature rigidity index theorem Fredholm family convex hypersurfaces

2026-07-10abs ↗pdf ↗

Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower boundmath.DG

Sharp bounds and parabolicity results for 3-manifolds with scalar curvature.

problem Understanding the spectrum and parabolicity of 3-manifolds with scalar curvature constraints.

method Established global results for complete three-dimensional manifolds under a topological assumption.

result Sharp upper bounds for the bottom spectrum and parabolicity results for manifolds with scalar curvature lower bounds.

3-manifolds scalar curvature parabolicity spectrum

2026-07-07abs ↗pdf ↗

Symplectically aspherical Kähler manifolds, scalar curvature, and the fundamental groupmath.GT

Study symplectically aspherical Kähler manifolds with unique properties.

problem Existence and properties of symplectically aspherical Kähler manifolds.

method Detailed study and analysis of geometric and topological features.

result Existence of symplectically aspherical Kähler manifolds with large fundamental groups.

symplectically aspherical Kähler manifolds fundamental group scalar curvature Kähler forms universal cover

2026-07-06abs ↗pdf ↗

Gromov's dihedral rigidity conjecture in dimension threemath.DG

Proof of Gromov's conjecture in 3D simplifies existing methods.

problem Gromov's dihedral rigidity conjecture on scalar curvature in 3D.

method Self-contained proof avoiding technical complications, shorter and more accessible than general case.

result Simplified proof of Gromov's conjecture in 3D.

Gromov's conjecture scalar curvature rigidity 3D shorter proof

2026-06-29abs ↗pdf ↗

Scalar-Flatness for Critical Metrics of the

L^2

-Scalar Curvature Functional in Dimensions

5\le n\le 9

math.DG

Researchers confirm scalar-flatness for critical metrics in 5-9 dimensions.

problem Verifying scalar-flatness for critical metrics in specific dimensions.

method Analyzing complete Riemannian manifolds with critical metrics of the

L^2

-scalar curvature functional.

result The conjecture that all complete noncompact critical metrics with finite energy are scalar-flat is confirmed for dimensions 5 to 9.

Scalar curvature Critical metrics Complete manifolds Dimension 5-9 Finite energy

2026-06-27abs ↗pdf ↗