Nick Edelen

I am an Assistant Professor at Notre Dame. I study problems in geometric analysis and geometric measure theory. Earlier, I was an NSF Fellow and CLE Moore instructor at MIT, under the sponsorshop of Tobias Colding; I was a PhD student at Stanford advised by Simon Brendle and coadvised by Brian White; I was an undergraduate at University of Edinburgh. My email is nedelen at nd dot edu. My office is 283 Hurley.

I am a coorganizer of our Geometry and Analysis seminar.

This spring 2025 I am teaching Graduate Differential Geometry. Past teaching.

I am currently supported by NSF grant DMS-2204301.

Papers

• Regularity of minimal surfaces with capillary boundary conditions (joint with Luigi De Masi, Carlo Gasparetto, and Chao Li) submitted (2024).
• Rectifiable Reifenberg and uniform positivity under almost calibrations (joint with Aaron Naber and Daniele Valtorta) submitted (2024).
• Uniqueness of regular tangent cones for immersed stable hypersurfaces (joint with Paul Minter) Arch. Ration. Mech. Anal., 248, 121 (2024). arxiv
• Improved regularity for minimizing capillary hypersurfaces (joint with Otis Chodosh and Chao Li) submitted (2024).
• The symmetric (log-)epiperimetric inequality and a decay-growth estimate (joint with Luca Spolaor and Bozhidar Velichkov) Calc. Var. PDE, 63, 2 (2024). arxiv
• A Liouville-type theorem for cylindrical cones (joint with Gabor Szekelyhidi) Comm. Pure. Appl. Math., 77:3557-3580 (2024). arxiv
• A strong maximum principle for minimizers of the one-phase Bernoulli problem (joint with Luca Spolaor and Bozhidar Velichkov) Indiana Univ. Math. J., 73:1061-1096 (2024). arxiv
• Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index Arch. Ration. Mech. Anal., 248, 65 (2022). arxiv
• A Bernstein-type theorem for minimal graphs over convex domains (joint with Zhehui Wang) Ann. Inst. H. Poincare Anal. Non Lineaire, 39:749-760 (2021). arxiv
• Regularity of free boundary minimal surfaces in locally polyhedral domains (joint with Chao Li) Comm. Pure. Appl. Math., 75:970-1031 (2021). arxiv
• Mean convex mean curvature flow with free-boundary (joint with Robert Haslhofer, Mohammad Ivaki, and Jonathan Zhu) Comm. Pure. Appl. Math., 75:767-817 (2020). arxiv
• Regularity of minimal surfaces near quadratic cones (joint with Luca Spolaor) Ann. of Math., 198:1013-1046 (2023). arxiv
• A note on the singular set of area-minimizing hypersurfaces Calc. Var. PDE 59:1-18 (2020). arxiv
• Effective Reifenberg theorems in Hilbert and Banach spaces (joint with Aaron Naber and Daniele Valtorta). Math. Ann. 372:1139-1218 (2018). arxiv
• The singular set of minimal surfaces near polyhedral cones (joint with Maria Colombo and Luca Spolaor) J. Differ. Geom. 120:411-503 (2022). arixv
• Quantitative stratification for some free-boundary problems (joint with Max Engelstein) Trans. Amer. Math. Soc., 371:2043-2072 (2019). arxiv
• Quantitative Reifenberg theorem for measures (joint with Aaron Naber and Daniele Valtorta) submitted (2016).
• The free-boundary Brakke flow J. Reine Angew. Math., 758:95-137 (2020). arxiv
• The PPW conjecture in curved spaces J. Funct. Anal., 272:849-865 (2017). arxiv
• Convexity estimates for mean curvature flow with free boundary Adv. Math., 294:1-36 (2016). arxiv
• Noncollapsing of Curve-Shortening Flow in Surfaces Int. Math. Res. Not. 2015:10143-10153 (2015).
• Constant mean curvature, flux conservation, and symmetry (joint with Bruce Solomon) Pacific J. Math., 274:53-72 (2015). arxiv

Other:

• Notes on Naber-Valtorta's discrete/rectifiable-Reifenberg, and their proof of finite rectifiability of the singular set (also, a measure theoretic version).
• Notes on Brian White's classes on mean curvature flow, and minimal surfaces (see also Otis's page).
• Notes on free boundary varifolds.