On-device research index

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

Trend · papers per month

count % of corpus

← all fields·11 papers on “riemannian manifolds” in Differential Geometry · 1 month

An integral inequality for compact Bach-flat

\mathcal{A}_{2}

-manifoldsmath.DG

Researchers prove a new inequality for special Riemannian manifolds.

problem Establishing a new integral inequality for a specific class of Riemannian manifolds.

method Developed a Catino-type integral inequality for closed Bach-flat A₂-manifolds.

result Derived rigidity results showing the manifold is either Einstein or a specific product space.

integral inequality Riemannian manifolds Bach-flat A₂ rigidity

2026-07-17abs ↗pdf ↗

On generalized

ξ

-Parallel Mapsmath.DG

Study on generalized ξ-parallel maps in Riemannian geometry.

problem Characterizing and understanding generalized ξ-parallel maps.

method Defined energy functional, derived first variation formula, and Euler-Lagrange equation.

result Established fundamental properties and relationships with harmonic and biharmonic maps.

ξ-parallel maps Riemannian manifolds energy functional Euler-Lagrange equation harmonic maps

2026-07-11abs ↗pdf ↗

Superwind and navigation of least time on Riemannian manifoldsmath.DG

This work analyzes minimum-time navigation on Riemannian manifolds using Finsler geometry.

problem Minimum-time navigation on Riemannian manifolds.

method Finsler geometry, introducing superwind concept, extending

(α, β)

-metrics.

result Time-minimizing geodesics and necessary/sufficient conditions for strong convexity.

minimum-time navigation Riemannian manifolds Finsler geometry superwind $(α

2026-07-05abs ↗pdf ↗

On the rigidity of Finslerian conformal circle-preserving transformationsmath.DG

Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.

problem Characterizing Finslerian manifolds without circle-preserving transformations.

method Analyzing critical points of conformal transformations to prove manifold rigidity.

result Compact Finslerian manifolds are Riemannian and conformally diffeomorphic to standard spheres, Euclidean spaces, or hyperbolic spaces.

Finslerian manifolds circle-preserving transformations rigidity conformal transformations critical points

2026-07-03abs ↗pdf ↗

On the rigidity of generalized

m

-quasi-Einstein manifolds of Yamabe-typemath.DG

Study on rigidity of special Riemannian manifolds.

problem Rigidity properties of generalized

m

-quasi-Einstein manifolds of Yamabe-type.

method Investigation of rigidity properties for the potential vector field in compact and non-compact settings.

result The potential vector field either vanishes identically or becomes a non-trivial Killing vector field under certain assumptions.

Riemannian manifolds rigidity generalized $m$-quasi-Einstein Yamabe-type potential vector field

2026-07-02abs ↗pdf ↗

The rigidity of conformal circle-preserving transformations on Berwaldian manifoldsmath.DG

Proves rigidity of certain transformations on specific geometric manifolds.

problem Rigidity of conformal circle-preserving transformations on Berwaldian manifolds.

method Analyzes properties of Berwaldian manifolds and flag curvatures.

result Rigidity condition for nontrivial conformal circle-preserving transformations.

Riemannian manifolds Berwaldian manifolds Conformal circle-preserving transformations Flag curvature Rigidity

2026-07-01abs ↗pdf ↗

Another look at a notion of fractional mass in codimension twomath.DG

Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.

problem Defining and studying fractional mass for codimension-two currents on manifolds.

method Energy minimization with Jacobian constraint, equi-coercivity, Γ-convergence, weak linking.

result Equivalence of two formulations of fractional mass, improved regularity for

s

-harmonic maps.

fractional mass codimension-two currents Riemannian manifolds equi-coercivity Γ-convergence

2026-07-01abs ↗pdf ↗

Gradient Estimates for Neumann Semigroups on Manifolds with Boundary under Unbounded Curvature Conditionsmath.DG

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

problem Gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

method Establishes Bismut-type formulas and gradient estimates for Feynman--Kac semigroups on Riemannian manifolds with boundary, under geometric conditions formulated in terms of Ricci curvature and second fundamental form.

result Derives pointwise gradient estimates for the Neumann semigroup under variable, possibly unbounded, lower curvature bounds.

Gradient estimates Neumann semigroups Riemannian manifolds Unbounded curvature Feynman--Kac semigroups

2026-06-30abs ↗pdf ↗

Compactness for minimal surfaces with injectivity radius bounded from belowmath.DG

Compact theorem for minimal surfaces with lower injectivity radius.

problem Proving compactness of minimal surfaces with lower injectivity radius.

method Variant of Choi--Schoen compactness theorem, focusing on injectivity radius.

result Proved compactness theorem for minimal surfaces.

minimal surfaces compactness injectivity radius Riemannian manifolds

2026-06-27abs ↗pdf ↗

Pogorelov type interior

C^2

estimate for sum Hessian quotient equations on Riemannian manifoldsmath.AP

Interior $C^{2}$ estimates for sum Hessian quotient equations on Riemannian manifolds

problem Interior

C^{2}

estimates for sum Hessian quotient equations on Riemannian manifolds

method Interior

C^{2}

estimates for sum Hessian quotient equations on Riemannian manifolds

result Interior

C^{2}

estimates at the center of a geodesic ball

Riemannian manifolds sum Hessian quotient equations Pogorelov type estimates

2026-06-25abs ↗pdf ↗

Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvaturemath.DG

Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.

problem Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvature

method Show that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of nonpositive constant sectional curvature is minimal and that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of positive constant sectional curvature has constant mean curvature.

result Partial affirmative answers to Chen's conjecture, generalized Chen's conjecture in hyperbolic spaces, and Balmuş-Montaldo-Oniciuc conjecture in spheres within the class of Wintgen ideal submanifolds.

biharmonic Wintgen ideal submanifolds Riemannian manifolds constant sectional curvature

2026-06-24abs ↗pdf ↗