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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·7 papers on “kähler manifolds” in Differential Geometry · 1 month

A Hadamard Formula for Equilibrium Envelopes under Parallel Deformationmath.CV

Formula identifies boundary flux for Kähler manifolds under parallel deformation.

problem Identifying boundary flux for Kähler manifolds under parallel deformation.

method One-sided Hadamard formula for normalized Monge-Ampère energy.

result Identifies boundary component as negative outward Anzellotti trace of divergence-measure flux current.

Kähler manifolds parallel deformation Hadamard formula Monge-Ampère energy boundary flux

2026-07-19abs ↗pdf ↗

Nonlinear Hodge correspondence for morphismsmath.DG

Study Higgs sections and flat sections for nonlinear harmonic bundles.

problem Equivalence of Higgs and flat sections for nonlinear harmonic bundles.

method Analyze harmonic vector bundles, generalize to sub-fibrations and morphisms.

result Vanishing of a degree obstruction for general nonlinear harmonic bundles.

Higgs sections flat sections nonlinear harmonic bundles Kähler manifolds fiber product

2026-07-15abs ↗pdf ↗

Asymptotic expansion of induced Grassmannian Chern forms and distribution of random degeneracy setsmath.CV

The paper studies the distribution of random degeneracy sets on complex manifolds.

problem Distribution of random degeneracy sets on compact Kähler manifolds.

method Asymptotic expansion of induced Grassmannian Chern forms, meromorphic transforms, and Wishart distribution.

result Normalized currents converge to curvature forms with quantitative estimates.

Grassmannian Chern forms Kähler manifolds Random degeneracy sets Wishart distribution

2026-07-13abs ↗pdf ↗

A Numerical Criterion for the 2-Hessian Equation on Compact Kähler Manifoldsmath.DG

Criterion for solvability of complex 2-Hessian equation on compact Kähler manifolds.

problem Solvability of complex 2-Hessian equation on compact Kähler manifolds.

method Nakai--Moishezon-type criterion associated with the complex 2-Hessian equation.

result Criterion equivalent to existence of a smooth 2-admissible representative in complex dimension three.

Hessian equation Kähler manifolds Nakai--Moishezon criterion Gauduchon class complex dimension three

2026-07-13abs ↗pdf ↗

Upper Bounds for Hessian Matrices of Positive Solutions to Heat Equations on Kähler Manifoldsmath.DG

The study sets limits on heat equation solutions' Hessians on curved spaces.

problem Bounding Hessians of positive solutions to heat equations on Kähler manifolds.

method Global and local upper bounds for Hessian matrices under curvature constraints.

result Improved bounds on Hessians for Riemannian manifolds with lower sectional curvature.

Hessian matrices Heat equations Kähler manifolds Curvature constraints Positive solutions

2026-07-10abs ↗pdf ↗

Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondencemath.DG

Introduces Poisson K-stability for Kähler manifolds and proves existence of constant scalar curvature structures.

problem Stability conditions for Poisson structures on Kähler manifolds.

method Infinite-dimensional momentum map techniques.

result Existence of constant scalar curvature symplectic generalized Kähler structures on Kähler-Einstein Fano manifolds.

Poisson K-stability Kähler manifolds constant scalar curvature momentum map string theory

2026-07-07abs ↗pdf ↗

Iterative construction of Hermitian-Einstein metrics on stable bundlesmath.DG

Iterative method finds Hermitian-Einstein metrics on stable bundles.

problem Finding Hermitian-Einstein metrics on stable bundles over Kähler or Gauduchon manifolds.

method Iterative construction using a specific metric update formula.

result Smooth convergence to a Hermitian-Einstein metric from any initial metric.

Hermitian-Einstein metrics stable bundles Kähler manifolds Gauduchon manifolds iterative construction

2026-06-29abs ↗pdf ↗