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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 “minimal surfaces” in Differential Geometry · 1 month

Singly periodic minimal Wente torus with endsmath.DG

New minimal surfaces found with spherical curvature lines.

problem Finding minimal surfaces with specific curvature lines.

method Constructing surfaces parametrized by rhombic lattices.

result Found new examples of minimal annuli with free boundaries.

minimal surfaces spherical curvature lines free boundary

2026-07-19abs ↗pdf ↗

Invariant solutions for the asymptotic Plateau problem in

\mathbb{H}^3

math.DG

Paper finds invariant solutions for Plateau problem in hyperbolic space.

problem Finding minimal surfaces with specific symmetries in hyperbolic space.

method Proved existence of foliations by invariant minimal surfaces, used to solve the Plateau problem.

result Existence of invariant minimal surfaces solving the asymptotic Plateau problem.

Plateau problem hyperbolic space minimal surfaces invariant asymptotic

2026-07-08abs ↗pdf ↗

Flat minimal tori and Lu's second-gap conjecturemath.DG

Flat minimal tori counterexamples refute Lu's second-gap conjecture.

problem Lu's second-gap conjecture about minimal surfaces in higher codimensions.

method Constructing closed embedded counterexamples for minimal surfaces.

result Constant values of

S+λ_2

realized by flat minimal tori are dense in

(2,3)

, refuting the conjecture.

minimal surfaces flat tori Lu's conjecture codimension counterexamples

2026-06-29abs ↗pdf ↗

Anisotropic Obstacle Problems for Minimal Surfaces: Regularity of the Free Boundary via the Cahn-Hoffman Transformmath.DG

Study anisotropic obstacle problem for minimal surfaces using Cahn-Hoffman transform.

problem Anisotropic obstacle problem for minimal surfaces.

method Cahn-Hoffman transform to convert to isotropic problem with generalized Robin boundary condition.

result Optimal regularity of the solution and

C^{1,1}

regularity of the free boundary.

anisotropic obstacle problem minimal surfaces Cahn-Hoffman transform regularity free boundary

2026-06-27abs ↗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 ↗

Existence of classical minimal surfaces in

4

and

5

-manifoldsmath.DG

Closed Riemannian 4 or 5-manifolds contain branched immersed closed minimal surfaces.

problem Existence of classical minimal surfaces in 4 and 5-manifolds

method Harmonic replacement method

result Proves the existence of branched immersed closed minimal surfaces in 4 and 5-manifolds

minimal surfaces 4-manifolds 5-manifolds harmonic replacement branched immersions

2026-06-23abs ↗pdf ↗

The linearized minimal surfaces problemmath.DG

Characterizes kernel of linearization for minimal surfaces problem

problem Characterizing kernel of linearization for minimal surfaces problem

method Show kernel consists of potential fields and TT fields

result In whole-space Euclidean decomposition, kernel consists of potential fields and TT fields

linearization minimal surfaces kernel potential fields TT fields

2026-06-23abs ↗pdf ↗