6 papers
Special Lagrangians with multiple isolated singularities
Bryan Dimler, Filippo Gaia
We extend the Caffarelli-Hardt-Simon perturbation argument for truncated regular minimal cones to the special Lagrangian setting and prove a bridge principle for regular special La…
Existence of constant mean curvature surfaces with controlled topology in 3-manifolds
Filippo Gaia, Xuanyu Li
We establish the existence of a non-trivial, branched immersion of a closed Riemann surface with constant mean curvature (CMC) into any closed, orientable 3-manifold $\math…
IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation
Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck +57
As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of…
Free boundary Hamiltonian stationary Lagrangian discs in
Filippo Gaia
Let be a smooth domain. We establish conditions under which a weakly conformal, branched -free boundary Hamiltonian stationary Lagrangian immersion o…
Hamiltonian stationary maps with infinitely many singularities
Filippo Gaia
For any we construct an Hamiltonian stationary Lagrangian map from a disc to with infinitely many Schoen-Wolfson singularities which is of class $C…
The fractional Hopf differential and a weak formulation of stationarity for the half Dirichlet energy
Filippo Gaia
We obtain a weak formulation of the stationarity condition for the half Dirichlet energy, which can be expressed in terms of a fractional analogous to the Hopf differential. As an…