Preprints and Publications

Preprints

  • [41] Revisiting generic mean curvature flow in R^3, with O. Chodosh, K. Choi and C. Mantoulidis (2024), [arXiv:2409.01463]
  • [40] On the Hamilton-Lott conjecture in higher dimensions, with A. Deruelle and M. Simon (2024), [arXiv:2403.00708]
  • [39] Mean curvature flow with generic low-entropy data II, with O. Chodosh and C. Mantoulidis (2023), [arXiv:2309.03856]
  • [38] Mean curvature flow with generic initial data II, with O. Chodosh and K. Choi (2023), [arXiv:2302.08409]
  • [37] Generic regularity for minimizing hypersurfaces in dimensions 9 and 10, with O. Chodosh and C. Mantoulidis (2023), [arXiv:2302.02253]
  • [36] Neck pinches along the Lagrangian mean curvature flow of surfaces, with J. Lotay and G. Székelyhidi (2022), [arXiv:2208.11054]
  • [35] Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds, with A. Deruelle and M. Simon (2022), [arXiv:2203.15313]
  • [34] Stability of neckpinch singularities, with N. Sesum (2020), [arXiv:2006.06118]

Publications

  • [33] Mean curvature flow from conical singularities, with O. Chodosh and J. Daniels-Holgate (2024), to appear in Invent. Math. [arXiv:2312.00759]
  • [32] Mean curvature flow with generic initial data, with O. Chodosh, K. Choi and C. Mantoulidis (2024), Invent. Math. 237 (2024), 121–2020 , [arXiv:2003.14334].
  • [31] Improved generic regularity of codimension-1 minimizing integral currents, with O. Chodosh and C. Mantoulidis, Ars Inven. Anal. (2024), Paper No. 3, 16 pp, [arXiv:2306.13191].
  • [30] Ancient solutions and translators of Lagrangian mean curvature flow, with J. Lotay and G. Székelyhidi, Publ. Math. Inst. Hautes Études Sci. (2024), [arXiv:2204.13863]
  • [29] A short proof of Allard's and Brakke's regularity theorems, with G. De Philippis and C. Gasparetto (2023),  Int. Math. Res. No. IMRN (2024), no. 9, 7594–7613, [arXiv:2306.02490]
  • [28] Huisken-Yau-type uniqueness for area-constrained Willmore spheres, with M. Eichmair, T. Körber and J. Metzger, Duke Math. J. 173 (2024), no. 9, 1677–1730, [arXiv:2204.04102]
  • [27] Mean curvature flow with generic low-entropy initial data, with O. Chodosh, K. Choi and C. Mantoulidis, Duke Math. J. 173 (2024), no. 7, 1269–1290, [arXiv:2102.11978]
  • [26] A relative entropy and a unique continuation result for Ricci expanders, with A. Deruelle, Comm. Pure Appl. Math. 76 (2023), no. 10, 2613–2692, [arXiv:2101.02638]
  • [25] Uniqueness of asymptotically conical tangent flows, with O. Chodosh, Duke Math. J. 170 (2021), no. 16, 3601–3657, [arXiv:1901.06369]. 
  • [24] Positive solutions to Schrödinger equations and geometric applications, with O. Munteanu and J. Wang, J. Reine Angew. Math. 774 (2021), 185–217, [arXiv:2007.07191].
  • [23] On the regularity of Ricci flows coming out of metric spaces, with A. Deruelle and M. Simon,  J. Eur. Math. Soc. (JEMS) 24 (2022), no. 7, 2233–2277., [arXiv:1904.11870].
  • [22] Ancient solutions in Lagrangian mean curvature flow, with B. Lambert and J.D. Lotay,  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 3, 1169–1205, [arXiv:1901.05383].
  • [21] Generic uniqueness of expanders with vanishing relative entropy, with A. Deruelle, Math. Ann. 377, No. 3-4, 1095-1127 (2020). [arXiv:1812:08504].
  • [20] Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds, Geom. Funct. Anal. 30 (2020), no. 1, 255–288, [arXiv:1802.00226].
  • [19] Remarks on the self-shrinking Clifford Torus, with C.G. Evans and J.D. Lotay, J. Reine Angew. Math. 765 (2020), 139–170, [arXiv:1802.01423].
  • [18] Local foliation of manifolds by surfaces of Willmore type, with T. Lamm and J. Metzger, Ann. Inst. Fourier (Grenoble) 70 (2020), no. 4, 1639–1662, [arXiv:1806.00465].
  • [17] Ricci flow from spaces with isolated conical singularities, with P. Gianniotis, Geom. Topol. 22 (2018), no. 7, 3925–3977, [arXiv:1610.09753].
  • [16] Consequences of strong stability of minimal submanifolds, with J.D. Lotay, Int. Math. Res. Not. IMRN, (2020) no. 8, 2352–2360, [arXiv:1802.03941].
  • [15] On short time existence for the planar network flow, with A. Neves and T. Ilmanen, J. Differ. Geom., 111 (1), (2019), [arXiv:1407.4756].
  • [14] A local regularity theorem for mean curvature flow with triple edges, with B. White, J. Reine Angew. Math. 758 (2020), 281–305, [arXiv:1605.06592].
  • [13] The half-space property and entire positive minimal graphs in M × R, with H. Rosenberg and J. Spruck, J. Differ. Geom., 95 (2), 321–336 (2013), [arXiv:1206.3499].
  • [12] Uniqueness of compact tangent flows in Mean Curvature Flow, J. Reine Angew. Math. (690), 163–172 (2014), [arXiv:1107.4643].
  • [11] Expanding solitons with non-negative curvature operator coming out of cones, with M. Simon, Math. Z. 275 (1-2), 625–639 (2013), [arXiv:1008.1408].
  • [10] Stability of Hyperbolic space under Ricci-flow, with O.C. Schnürer and M. Simon, Comm. Anal. Geom. 19, No. 5, 1023–1047 (2011), [arXiv:1003.2107].
  • [9] Foliations of asymptotically flat spacetimes by surfaces of Willmore type, with T. Lamm and J. Metzger, 2009, Math. Ann. 350, No. 1, 1–78 (2011), [arXiv:0903.1277].
  • [8] Evolution of convex lens-shaped networks under curve shortening flow, with O.C. Schnürer, M. Saez, A. Azouani, M. Georgi, J. Hell, N. Jangle, A. Koeller, T. Marxen, S. Ritthaler, and B. Smith, Trans. Amer. Math. Soc. 363, No. 5, 2265–2294 (2011), [arXiv:0711.1108].
  • [7] Stability of Euclidean space under Ricci-flow, with M. Simon and O.C. Schnürer, Comm. Anal. Geom. 16, No. 1, 127–158 (2008), [arXiv:0706.0421].
  • [6] No mass drop for mean curvature flow of mean convex hypersurfaces, with J. Metzger, Duke Math. J., Vol. 124 (2) (2008), 283–312, [arXiv:math/0610217].
  • [5] Nonlinear evolution by mean curvature and isoperimetric inequalities, J. Differ. Geom. 79 (2008), 197–241, [arXiv:math/0606675].
  • [4] Self-similarly expanding networks to curve shortening flow, with O.C. Schnürer, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. VI (2007), 511-528, [arXiv:math/0702698].
  • [3] Stability of translating solutions to mean curvature flow, with J. Clutterbuck and O. C. Schnürer, Calc. Var. Partial Differential Equations 29 (2007), no. 3, 281–293, [arXiv:math/0509372].
  • [2] Convexity estimates for flows by powers of the mean curvature, appendix with O.C. Schnürer, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. V (2006), 261–277, [pdf].
  • [1] Evolution of convex hypersurfaces by powers of the mean curvature, Math. Z. 251 (2005), no. 4, 721–733, [pdf].

Surveys

  • [1] Evolution of networks with multiple junctions, survey, with C. Mantegazza, M. Novaga and A. Pluda, (2016), to appear in Astérisque, [arXiv:1611.08254].