University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Regularity of Lagrangian flows over RCD*(K, N) spaces
Journal für die reine und angewandte Mathematik (Crelles Journal) issue 765 volume 2020 page 171-203 (1 August 2020)
Constancy of the Dimension for RCD(
) Spaces via Regularity of Lagrangian Flows
Communications on Pure and Applied Mathematics issue 6 volume 73 page 1141-1204 (1 June 2020)
Polya-Szego inequality and Dirichlet $p$-spectral gap for non-smooth
spaces with Ricci curvature bounded below
Journal de Mathematiques Pures et Appliquees volume 137 page 238-274 (1 May 2020) Full text available
Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces
Analysis and Geometry in Metric Spaces issue 1 volume 7 page 158-178 (30 September 2019)
Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces
Geometric and Functional Analysis issue 4 volume 29 page 949-1001 (1 July 2019)
My main research topic are non smooth spaces with lower curvature bounds, at the interface between Analysis and Geometry.
Mainly I am interested on the study of geometric and functional inequalities on these spaces and on their fine structure.
Prizes, awards, and scholarships:
Benedetto Sciarra Prize of the Scuola Normale Superiore of Pisa (2019).
Major / recent publications:
E. Bruè, D. Semola, Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows, Comm. Pure Appl. Math., 73: 1141-1204, doi:10.1002/cpa.21849.
L. Ambrosio, E. Bruè, D. Semola, Rigidity of the 1-Bakry-Émery inequality and sets of finite perimeter in RCD spaces, Geom. Funct. Anal. 29 (2019), no. 4, 949–1001.
E. Bruè, A. Naber, D. Semola, Boundary regularity and stability for spaces with Ricci bounded below, preprint ArXiv.