Sven Hirsch

Publications

My research can also be found on Google Scholar.

1. Classification of Maximally Charged Black Holes, joint with Yiyue Zhang, 2026, arXiv
2. Stable 2-systoles, scalar curvature and spin^c comass bounds, joint with Simone Cecchini and Rudolf Zeidler, 2026, arXiv
3. On a Variant of the Penrose Conjecture, joint with Yipeng Wang, 2026, arXiv
4. The Hyperboloidal and Spacetime Positive Mass Theorem in all dimensions, joint with Marcus Khuri, Martin Lesourd and Yiyue Zhang, 2026, arXiv
5. The Spacetime Positive Mass Theorem with Multiple Time Dimensions, joint with Alec Payne and Yiyue Zhang, 2026, arXiv
6. The lock principle for scalar curvature, joint with Georg Frenck and Bernhard Hanke, 2026, arXiv
7. Surgery and total mean curvature, joint with Georg Frenck and Bernhard Hanke, 2026, arXiv
8. A universal Bochner formula for scalar curvature, 2026, arXiv
9. Causal character of imaginary Killing spinors and spinorial slicings, joint with Yiyue Zhang, 2025, arXiv
10. Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers, joint with Lan-Hsuan Huang, 2025, arXiv
11. Rigidity of Asymptotically Hyperboloidal Initial Data Sets with Vanishing Mass, joint with Hyun Chul Jang and Yiyue Zhang, 2025, Comm. Math. Phys., arXiv
12. Rigidity of spin fill-ins with non-negative scalar curvature, joint with Simone Cecchini and Rudolf Zeidler, 2024, arXiv
13. Initial data sets with vanishing mass are contained in pp-wave spacetimes, joint with Yiyue Zhang, 2025, J. Eur. Math. Soc., arXiv
14. Stability of Llarull’s theorem in all dimensions, joint with Yiyue Zhang, 2024, Adv. Math., arXiv
15. Uniqueness of blowups for forced mean curvature flow, joint with Jonathan Zhu, 2023, Int. Math. Res. Not., arXiv
16. Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem, joint with Demetre Kazaras, Marcus Khuri and Yiyue Zhang, 2023, Int. Math. Res. Not., arXiv
17. Hawking mass monotonicity for initial data sets, 2025, Asian J. Math., arXiv
18. Rigid comparison geometry for Riemannian bands and open incomplete manifolds, joint with Demetre Kazaras, Marcus Khuri and Yiyue Zhang, 2022, Math. Ann., arXiv
19. A generalization of Geroch’s conjecture, joint with Simon Brendle and Florian Johne, 2023, Comm. Pure Appl. Math., arXiv
20. Monotone quantities of p-harmonic functions and their applications, joint with Pengzi Miao and Luen-Fai Tam, 2022, Pure Appl. Math. Q., arXiv
21. The case of equality for the spacetime positive mass theorem, joint with Yiyue Zhang, J. Geom. Anal., 2022, arXiv
22. Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations, joint with Demetre Kazaras and Marcus Khuri, J. Differential Geom., 2021, arXiv
23. On the Moduli Space of Asymptotically Flat Manifolds with Boundary and the Constraint Equations, joint with Martin Lesourd, Comm. Anal. Geom., 2021, arXiv
24. Mass of asymptotically flat 3-manifolds with boundary, joint with Pengzi Miao and Tin-Yau Tsang, Comm. Anal. Geom., 2021, arXiv
25. Spacetime Harmonic Functions and Applications to Mass, joint with Hubert Bray, Demetre Kazaras, Marcus Khuri and Yiyue Zhang, SIGMA, 2021, arXiv
26. Contracting convex surfaces by mean curvature flow with free boundary on convex barriers, joint with Martin Li, Asian J. Math., 2023, arXiv
27. Flatly Foliated Relativity, joint with Hubert Bray, Benjamin Hamm, James Wheeler and Yiyue Zhang, Pure Appl. Math. Q., 2019, arXiv
28. A Positive Mass Theorem for Manifolds with Boundary, joint with Pengzi Miao, Pac. J. Math., 2019, arXiv

Professional Activities

Seminars and conferences organized

• Lonavala Geometry Festival.
• Workshop Connections among spin geometry, minimal surfaces and relativity at the Chennai Mathematical Institute.
• Learning seminar on String Theory.

Teaching

• I am currently teaching Modern Analysis (Math 4061). Information about the course can be found here.
• In 2026, I taught a minicourse on spinors and gravitational waves at Tsinghua and gave a lecture series at the University of Padova.
• I taught a minicourse on spinors, gravitational waves and black holes in Copenhagen. The lecture notes can be found here: Spinors and Spacetime Harmonic Functions (PDF) .
• I am organizing an undergraduate geometry and mathematical relativity reading course. If you would like to participate, please send me an email.

Outreach

• My research was featured in Quanta and appeared on The Late Show with Stephen Colbert .
• Sofya Kovalevskaya Day.

Geometric Analysis Seminar

The seminar takes place on Fridays from 3 to 4 pm in Math 507.