Mohammad N. Ivaki

Mohammad N. Ivaki

Associate Professor, Technische Universität Wien, Austria

Interests: Geometric flows, Partial Differential Equations, Convex geometry

Email: mohammad.ivaki@tuwien.ac.at

Selected Publications

Capillary curvature images (with Y. Hu), arXiv (2025).
Capillary Christoffel-Minkowski problem (with Y. Hu, J. Scheuer), arXiv (2025).
Stability of the cone-volume measure with near constant density (with Y. Hu), IMRN (2025).
Prescribed L_p curvature problem (with Y. Hu), Adv. Math. 442(2024): #109566.
On the uniqueness of solutions to the isotropic L_p dual Minkowski problem (with Y. Hu), Nonlinear Anal. 241(2024): #113493.
Uniqueness of solutions to a class of non-homogeneous curvature problems, arXiv (2023).
L^p-Minkowski problem under curvature pinching (with E. Milman), IMRN 10(2024): 8638-8652.
On the classification of ancient solutions to curvature flows on the sphere (with P. Bryan, J. Scheuer), Annali SNS 5(2024): 53-76.
Uniqueness of solutions to a class of isotropic curvature problems (with E. Milman), Adv. Math. 435(2023): #109350.
Christoffel-Minkowski flows (with P. Bryan, J. Scheuer), Trans. Amer. Math. Soc. 376(2023): 2373-2393.
Constant rank theorems for curvature problems via a viscosity approach (with P. Bryan, J. Scheuer), Cal. Var. PDE 62(2023): #98.
On the stability of the L_p-curvature, J. Funct. Anal. 283(2022): #109684.
Mean convex mean curvature flow with free boundary (with N. Edelen, R. Haslhofer, J. Zhu), Comm. Pure Appl. Math. 75(2022): 767-817.
Orlicz-Minkowski flows (with P. Bryan, J. Scheuer), Calc. Var. PDE 60(2021): #41.
Parabolic approaches to curvature equations (with P. Bryan, J. Scheuer), Nonlinear Anal. 203(2021): #112174.
Negatively curved three-manifolds... and the cross curvature flow (with P. Bryan, J. Scheuer), LMS Lecture Note Ser. (2020): 75-97.
Iterations of curvature images, Mathematika 66(2020): 640-648.
Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds (with P. Bryan, J. Scheuer), Crelle's 764(2020): 71-109.
Deforming a hypersurface by principal radii of curvature and support function, Calc. Var. PDE 58(2019): #1.
A unified flow approach to smooth, even L_p-Minkowski problems (with P. Bryan, J. Scheuer), Analysis & PDE 12(2019): 259-280.
A local uniqueness theorem for minimizers of Petty's conjectured projection inequality, Mathematika 64(2018): 1-19.
The second mixed projection problem and the projection centroid conjectures, J. Funct. Anal. 272(2017): 5144-5161.
Deforming a hypersurface by Gauss curvature and support function, J. Funct. Anal. 271(2016): 2133-2165.
The planar Busemann-Petty centroid inequality and its stability, Trans. Amer. Math. Soc. 368(2016): 3539-3563.
Centro-affine normal flows on curves: Harnack estimates and ancient solutions, Ann. I. H. Poincaré 32(2015): 1189-1197.
Stability of the Blaschke-Santaló inequality in the plane, Monatsh. Math. 177(2015): 451-459.

Selected Talks

02.2025 Poděbrady Castle, Czechia.
01.2025 Department Colloquium, TU Wien, Austria.
07.2024 Bridging PDE and Geometric Flows (3 lectures), Cardiff University, Wales.
06.2024 Current Trends in Geometric Flows, Montreal, Canada.
06.2024 41st Süddeutsches Kolloquium über Differentialgeometrie, Frankfurt, Germany.
05.2024 Conference on Convex Geometry and Related PDEs, Hunan University, China.
04.2024 Warwick Analysis Seminar, Warwick University, UK.
12.2023 Geometric Analysis Seminar, Vienna University, Austria.
11.2023 Geometry Seminar, Friedrich-Schiller-Universität, Jena, Germany.
10.2023 Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.
10.2020 Geometric Analysis Seminar, University of Toronto, Canada.
12.2019 CMS Winter Meeting, Geometric Analysis, Toronto, Canada.
11.2019 Geometry & Topology Seminar, University of Toronto, Canada.
02.2019 Department Colloquium, University of Bath, England.
10.2018 Geometric Analysis Colloquium, Fields Institute, Canada.
03.2018 Workshop in Geometric Analysis, CRM, Montreal, Canada.
12.2017 CMS Winter Meeting, Geometric Analysis, Waterloo, Canada.
09.2017 Analysis and Applied Math Seminar, University of Toronto, Canada.
02.2017 Analysis Seminar, Concordia University, Montreal, Canada.
02.2017 Geometric Analysis Seminar, McGill University, Montreal, Canada.
11.2015 Leibniz Universität, Hannover, Germany.
11.2015 PDE Seminar, Konstanz University, Germany.
09.2015 Affine Geometric Analysis, Oaxaca, Mexico.
09.2013 Conference on Convex Geometry, Castro Urdiales, Spain.
05.2013 XVI-th ISM-Quebec Student Conference, Montreal, Canada.
04.2012 Workshop on Convexity and Asymptotic Geometric Analysis, CRM, Montreal, Canada.

Awards and Recognitions

11.2022 Austrian Science Fund, Principal Investigator, Project P36545.
2017 Jerrold E. Marsden Fellowship, Fields Institute.
2014 Austrian Science Fund, Lise Meitner Program.
2013 Carl Herz Prize, The Institut des sciences mathématiques.
2006 Silver Medal: 30th Mathematics Competition for University Students, Tafresh, Iran.
2005 Silver Medal: 29th Mathematics Competition for University Students, Mazandaran, Iran.