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.

• Stability of ALE Ricci-flat manifolds under Ricci flow (with Klaus Kröncke) Submitted.

• Existence of expanders of the harmonic map flow (with Tobias Lamm) Submitted.

• A relative entropy for expanders of the harmonic map flow Submitted.