From the 1 of 5 linked papers with an AI index.
5 papers
Special Lagrangians with multiple isolated singularities
Bryan Dimler, Filippo Gaia
The paper extends a perturbation technique to construct special Lagrangian submanifolds in \(\mathbb{C}^m\) that have multiple prescribed isolated conical singularities, using a br…
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…
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 $\mat…
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 …
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…