Christos Mantoulidis

Source: Mathematisches Forschungsinstitut Oberwolfach.
License: Attribution-Share Alike 2.0 Germany.

Rice University, Department of Mathematics

christos.mantoulidis@rice.edu

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• Papers
• Reports
• Notes
• Theses
• Conferences
• Support
• Background

Papers

• Generic regularity for minimizing hypersurfaces in dimension 11 with O. Chodosh, F. Schulze, Z. Wang. Submitted.
• Almgren's three-legged starfish with J. Marx-Kuo. Submitted.
• Revisiting generic mean curvature flow in R³ with O. Chodosh, K. Choi, F. Schulze. J. Reine Angew. Math.. To appear in special bicentennial issue.
• Mean curvature flow with generic low-entropy initial data II with O. Chodosh, F. Schulze. Duke Math. J.. To appear.
• Improved generic regularity of codimension-1 minimizing integral currents with O. Chodosh, F. Schulze. Ars Inven. Anal., May 2024.
• Generic regularity for minimizing hypersurfaces in dimensions 9 and 10 with O. Chodosh, F. Schulze. Submitted.
• Double-well phase transitions are more rigid than minimal hypersurfaces. Proc. Am. Math. Soc., vol. 152 (2024), 1301-1308.
• Decomposing 4-manifolds with positive scalar curvature with R. H. Bamler, C. Li. Adv. Math., vol. 430 (2023), 109231.
• The p-widths of surfaces with O. Chodosh. Publ. Math. IHÉS, vol. 137 (2023), 245-342.
• Metrics with λ₁(-Δ+kR) >= 0 and flexibility in the Riemannian Penrose Inequality with C. Li. Commun. Math. Phys., vol. 401 (2023), 1831-1877.
• Mean curvature flow with generic low-entropy initial data with O. Chodosh, K. Choi, F. Schulze. Duke Math. J., vol. 173 (2024), 1269-1290.
• Variational aspects of phase transitions with prescribed mean curvature. Calc. Var. Partial Differ. Equ., vol. 61 (2022), no. 2, article 43.
• Mean curvature flow with generic initial data with O. Chodosh, K. Choi, F. Schulze. Invent. Math., vol. 237 (2024), 121-220.
• Ancient gradient flows of elliptic functionals and Morse index with K. Choi. Am. J. Math., vol. 144 (2022), no. 2, 541-573.
• Minimal hypersurfaces with arbitrarily large area with O. Chodosh. Int. Math. Res. Not., vol. 2021 (2021), no. 14, 10841-10847.
• Capacity, quasi-local mass, singular fill-ins with P. Miao, L.-F. Tam. J. Reine Angew. Math., vol. 2020 (2020), no. 768, 55-92.
• Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates with O. Chodosh. Ann. Math., vol. 191 (2020), no. 1, 213-328.
• Positive scalar curvature with skeleton singularities with C. Li. Math. Ann., vol. 374 (2019), no. 1, 99-131. [Known Misprints]
• Allen-Cahn min-max on surfaces. J. Differ. Geom., vol. 117 (2021), no. 1, 93-135.
• Total mean curvature, scalar curvature, and a variational analog of Brown-York mass with P. Miao. Commun. Math. Phys., vol. 352 (2017), no. 2, 703-718.
• On the Bartnik mass of apparent horizons with R. Schoen. Class. Quantum Gravity, vol. 32 (2015), no. 20, 205002. Appeared on IOPselect 2015, a special edition of articles, on the basis of substantial advances, a high degree of novelty, and/or impact on future research.

Reports

• Minimal surfaces and the Allen-Cahn equation on 3-manifolds. Proceedings of the 2024 International Congress of Basic Science, to appear.
• Improved generic regularity of minimizing hypersurfaces. MFO Reports, No. 29 (2023), to appear.
• Decomposing 4-manifolds with positive scalar curvature. MFO Reports, No. 28 (2022), 1593-1595.
• The p-widths of a surface. MFO Reports, No. 35 (2021), 1900-1902.
• Metrics with λ₁(-Δ+kR) >= 0 and flexibility in the Riemannian Penrose Inequality. MFO Reports, No. 30 (2021), 1637-1640.
• Ancient gradient flows of elliptic functionals and Morse index. MFO Reports, No. 34 (2019), 2055-2058.
• Minimal surfaces and the Allen-Cahn equation on 3-manifolds. MFO Reports, No. 27 (2018), 1658-1661; also, No. 35 (2018), 2113-2116.
• Mean curvature deficit and a quasi-local mass with P. Miao. Harvard University CMSA Series in Mathematics, vol. 1 (2017), Nonlinear analysis in geometry and applied mathematics, 99-107.
• The curvature on a black hole boundary. CQG+ Insight Piece, 2015.

Notes

• T. H. Colding and W. P. Minicozzi's blowup uniqueness and Łojasiewicz inequalities.
• Richard Schoen's lectures on minimal submanifolds with D. Cheng, C. Li.
• Yi Wang's lectures on harmonic analysis and isoperimetric inequalities with D. Cheng, O. Chodosh, N. Edelen, C. Henderson, P. Hintz.
• Richard Bamler's lectures on Ricci flow with O. Chodosh.
• Brian White's lectures on minimal surfaces with O. Chodosh.

Theses

• Geometric variational problems in mathematical physics. Advisor: Richard Schoen. Doctoral thesis. [Known Misprints]
• Regularity of hypersurfaces in Rⁿ⁺¹ moving by mean curvature flow. Advisor: Leon Simon. Undergraduate honors thesis.
  The exposition follows Klaus Ecker's Regularity Theory for Mean Curvature Flow.

Conferences

Organizing in the future:

• Partial Differential Equations with I. Fraser, T. Lamm, X. Ros Oton. Oberwolfach, Germany, July 25-30, 2027.
• Moduli Theory in Differential Geometry and Analysis with I. Alonso Lorenzo, B. Hanke, M. Upmeier. Oberwolfach, Germany, January 3-8, 2027.
• Rice Dynamics and Geometry Conference with F. Arana Herrera, D. Fisher, J. Marx-Kuo. Rice University, USA, April 10-12, 2026.

Organized in the past:

• Geometric moduli spaces - rigidity, genericity, stability with I. Alonso Lorenzo, B. Hanke, M. Upmeier. ICMS, Scotland, May 19-23, 2025.
• Simons Workshop on Geometric Analysis at Courant with C. Li, V. Tosatti. Courant Institute (NYU), USA, May 9-11, 2025.
• Geometry of Scalar Curvature 2019 with B. Hanke, P. Piazza, T. Schick, C. Sormani. Il Palazzone Cortona, Italy, July 8-12, 2019.

Support

• NSF Grant DMS-1905165/2050120/2147521.
• NSF Grant DMS-2403728.
• AMS/Simons travel grant.

Background

• Associate Professor, Rice University, now.
• Assistant Professor, Rice University.
• Assistant Professor, Brown University.
• CLE Moore Instructor, Massachusetts Institute of Technology.
• PhD, Stanford University.
• BSc, Stanford University.