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 Fall 2024 I am teaching Calc III and Real Analysis. Past teaching.
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., to appear. (2024).
- 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
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