Travaux
My research interest is in differential geometry and partial differential equations. More precisely, I have been mainly focused on the study of Geometric Flows on non compact manifolds and especially on the geometry at infinity of self-similar solutions (solitons) of the (Kahler-)Ricci Flow, Mean Curvature Flow and the Harmonic Map Heat Flow.
- PhD work: Géométrie à l'infini de certaines variétés non compactes.
- Steady gradient Ricci soliton with curvature in L1 Comm. Anal. Geom. 20 (2012), no. 1, 31-53.
- Structure at infinity of expanding gradient Ricci soliton (with Chih-Wei Chen) Asian Journal of mathematics (2015), Vol. 19, no. 5.
- Rapport asymptotique de courbure, courbure positive et non effondrement Actes de Séminaire de Théorie Spectrale et Géométrie 2011_2012.
- Stability of non compact steady and expanding gradient Ricci solitons Calculus of variations and PDE's (2015).
- Asymptotic estimates and compactness of expanding gradient Ricci solitons Annali Della Scuola Normale Superiore Di Pisa, Volume XVI, serie V, June 2017.
- Smoothing out positively curved metric cones by Ricci expanders Geometric and Functional Analysis 26 (2016), 188-249.
- Unique continuation at infinity for conical Ricci expanders International Mathematical Research Notices, 2016, doi: 10.1093/imrn/rnw110.
- Weak stability of Ricci expanders with positive curvature operator (with Tobias Lamm) Matematische Zeitschrift, Nov. 2016, p. 1-35, doi:10.1007/s00209-016-1791-x.
- Expanding Kähler-Ricci solitons coming out of Kähler cones (with Ronan Conlon) Journal of Differential Geometry. Vol. 115. (2020) 303 365.
- Stability of ALE Ricci-flat manifolds under Ricci flow (with Klaus Kröncke) The Journal of geometric analysis, 1-42, (2020), DOI : 10.1007/s12220-020-00376-4.
- Existence of expanders of the harmonic map flow (with Tobias Lamm) Accepted for publication in Annales de l’ École Normale Supérieure.
- A relative entropy for expanders of the harmonic map flow Communications in Partial Differential Equations, Vol. 44, (2019), Issue 12.
- Generic uniqueness of expanders with vanishing relative entropy (with Felix Schulze) Mathematische Annalen, 377 (2020), no. 3-4, 1095-1127 DOI: 10.1007/s00208-020-02004-6.
- On the regularity of Ricci flows coming out of metric spaces (with Felix Schulze and Miles Simon) Accepted for publication in Journal of European Mathematical Society. (January 2020).
- Classification results for expanding and shrinking gradient Kahler-Ricci solitons (with Ronan Conlon and Song Sun) Submitted. arXiv:1904.00147
- Steady gradient Kahler-Ricci solitons on crepant resolutions of Calabi-Yau cones (with Ronan Conlon) Submitted. arXiv:2006.03100
- A Lojasiewicz inequality for ALE Ricci-flat metrics (with Tristan Ozuch) Submitted. arXiv:2007.09937
- A relative entropy and a unique continuation result for Ricci expanders (with Felix Schulze) Submitted. arXiv:2101.02638
- Dynamical (in)stability of Ricci-flat ALE metrics along the Ricci flow (with Tristan Ozuch) Submitted. arXiv:2104.10630