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 geometric analysis seminar.
This spring 2022 I am not teaching. Past teaching.
- A strong maximum principle for minimizers of the one-phase Bernoulli problem (joint with Luca Spolaor, and Bozhidar Velichkov) preprint (2022).
- Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index Arch. Ration. Mech. Anal., to appear (2022).
- 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) submitted (2019).
- 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