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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.

168,786 papers · 148 categories

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10 results for “hypercritical”

Hypercritical deformed Hermitian-Yang-Mills equation revisitedmath.DG

Study resolves conjectures on hypercritical deformed Hermitian-Yang-Mills equation.

problem Resolving conjectures on hypercritical deformed Hermitian-Yang-Mills equation.

method Study compact Kähler manifolds and resolves conjectures of Collins-Yau.

result Resolves two conjectures of Collins-Yau.

Hermitian-Yang-Mills equation compact Kähler manifolds conjectures hypercritical

2022-06-01abs ↗pdf ↗

Hypercritical deformed Hermitian-Yang-Mills equationmath.DG

Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.

problem Existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation.

method Introduce coerciveness and properness of the J-functional on almost calibrated (1,1)-forms.

result Equivalence of coerciveness and properness to the existence of solutions.

Hermitian-Yang-Mills equation compact Kähler manifold coerciveness properness solutions

2021-07-28abs ↗pdf ↗

Collapsing of the line bundle mean curvature flow on Kähler surfacesmath.DG

Study on line bundle flow on Kähler surfaces converging to a singular solution.

problem Analyzing the mean curvature flow on Kähler surfaces.

method Investigates the flow under hypercritical phase and semipositivity conditions.

result The flow converges to a singular solution away from curves of negative self-intersection.

line bundle mean curvature flow Kähler surfaces deformed Hermitian-Yang-Mills equation Kempf-Ness type functional blowup of Kähler surfaces

2019-12-31abs ↗pdf ↗

The space of almost calibrated

(1,1)

forms on a compact Kähler manifoldmath.DG

Study of geometric properties of almost calibrated forms on Kähler manifolds.

problem Understanding the geometry of almost calibrated

(1,1)

forms on compact Kähler manifolds.

method Investigates the infinite dimensional Riemannian manifold structure, CAT(0) geodesic metric space, and geodesics of the space of almost calibrated forms.

result The space of almost calibrated forms is an infinite dimensional Riemannian manifold with non-positive sectional curvature and CAT(0) geodesic metric space.

Kähler manifolds almost calibrated forms Riemannian manifold CAT(0) space geodesics

2020-02-05abs ↗pdf ↗

Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flowmath.AP

The paper proves Hessian estimates for specific geometric flows.

problem Proving interior Hessian estimates for specific geometric flows.

method Proved interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow.

result Extended results to a broader class of Lagrangian mean curvature type equations.

Hessian estimates Lagrangian mean curvature flow shrinkers expanders translators

2024-03-12abs ↗pdf ↗

The Cauchy-Dirichlet problem for parabolic deformed Hermitian-Yang-Mills equationmath.DG

Paper solves a complex equation for smooth domains.

problem Investigates a specific type of parabolic equation in complex domains.

method Uses J-functional to prove solution convergence.

result Proves the convergence of solutions to the equation.

parabolic equation Hermitian-Yang-Mills convergence J-functional smooth domain

2022-12-24abs ↗pdf ↗

The deformed Hermitian-Yang-Mills equation on almost Hermitian manifoldsmath.DG

Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.

problem Existence of solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.

method Derive a priori estimates under the existence of an admissible

\mathcal{C}

-subsolution; prove existence of solutions under the condition of existence of a supersolution.

result Proves existence of solutions for the deformed Hermitian-Yang-Mills equation.

deformed Hermitian-Yang-Mills equation almost Hermitian manifolds a priori estimates existence of solutions

2020-11-28abs ↗pdf ↗

Deformed Hermitian Yang-Mills equation on rational homogeneous varietiesmath.DG

The paper solves the dHYM equation on rational homogeneous varieties using Lie theory.

problem Solving the deformed Hermitian Yang-Mills equation on rational homogeneous varieties.

method Using Lie theory to describe the Lagrangian phase and characterize solutions.

result Characterization of all supercritical and hypercritical homogeneous solutions of the dHYM equation.

deformed Hermitian Yang-Mills equation rational homogeneous varieties Lie theory Kähler metrics slope semistability

2023-04-04abs ↗pdf ↗

Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphsmath.AP

The paper proves optimal smoothness for certain Lagrangian graphs with specific Hölder continuity.

problem Optimal regularity for Hölder continuous Hamiltonian stationary Lagrangian graphs.

method Establishing smoothness conditions based on Hölder exponent and Lagrangian phase properties.

result Smoothness of graphs is achieved when Hölder exponent is strictly greater than 1/3 and Lagrangian phase is supercritical.

Hamiltonian stationary Lagrangian graphs Hölder continuity Optimal regularity Smoothness conditions

2025-10-26abs ↗pdf ↗

Moment maps, nonlinear PDE, and stability in mirror symmetrymath.DG

We study the deformed Hermitian-Yang-Mills (dHYM) equation, which is mirror to the special Lagrangian equation, from the variational point of view via an infinite dimensional GIT problem mirror to Thomas' GIT picture for special Lagrangians. This gives rise to infinite dimensional manifold $\mathcal{H}$ mirror to Solom…

2018-11-12abs ↗pdf ↗