Lorenzo Sarnataro

Research

1. On the Gage–Hamilton–Grayson Theorem for free boundary curves
   (Joint with Yueheng Bao) arXiv:2610.09557 – 14 pages

2. Regularity and compactness theory of stable free-boundary minimal hypersurfaces
   (Joint with Costante Bellettini, Martin Li, and Davide Parise) arXiv:2610.09596 – 61 pages

3. Boundary behaviour of stable Allen–Cahn limit-interfaces in Riemannian manifolds
   (Joint with Martin Li and Davide Parise) arXiv:2610.04833 – 60 pages

4. Second order estimates on transition layers for the Allen–Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers
   (Joint with Akashdeep Dey, Wenkui Du, and Davide Parise) arXiv:2609.32829 – 107 pages

5. Existence of free boundary minimal disks in convex regions
   (Joint with Douglas Stryker, Zhichao Wang, and Xin Zhou) arXiv:2606.02396 – 22 pages

6. Index, intersections, and multiplicity of min-max geodesics
   (Joint with Jared Marx-Kuo and Douglas Stryker) arXiv:2410.02580 – Advances in Mathematics. Volume 502 (2026), Part C. Article 111193, pp. 1-46

7. Boundary behavior of limit-interfaces for the Allen–Cahn equation on Riemannian manifolds with Neumann boundary condition
   (Joint with Martin Li and Davide Parise) arXiv:2312.07210 – Arch. Ration. Mech. Anal. 248, 124 (2024), pp. 1-43

8. Existence of closed embedded curves of constant curvature via min-max
   (Joint with Douglas Stryker) arXiv:2306.04840 – Reine Angew. Math. (Crelle’s Journal), vol. 2026, no. 831, pp. 185-211

9. Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
   (Joint with Douglas Stryker) arXiv:2304.02722 – Cambridge Journal of Mathematics, Vol. 13 (2025), no. 3, pp. 609-706

Talks

Teaching

University of Toronto

At Princeton University: