Travaux
My research interest is in differential geometry and partial differential equations. More precisely, I have been so far mainly focused on the study of Ricci Flow on non compact manifolds and especially on the geometry at infinity of self-similar solutions (Ricci solitons) of the Ricci 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
Caclulus 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) To appear in Journal of Differential of Geometry.
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Stability of ALE Ricci-flat manifolds under Ricci flow (with Klaus Kröncke) Submitted.
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Existence of expanders of the harmonic map flow (with Tobias Lamm) Submitted.
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A relative entropy for expanders of the harmonic map flow Submitted.