List of publications
Inequivalent complexity criteria for free boundary minimal surfaces (with G. Franz)
Contractibility results for certain spaces of Riemannian metrics on the disc (with D. Wu)
Constrained deformations of positive scalar curvature metrics (with C. Li)
Bubbling analysis and geometric convergence results for free boundary minimal surfaces (with L. Ambrozio, R. Buzano and B. Sharp)
Journal de l'École Polytechnique — Mathématiques, 6 (2019), 621-664.
Geometric convergence results for closed minimal surfaces via bubbling analysis (with L. Ambrozio, R. Buzano and B. Sharp)
Compactness analysis for free boundary minimal hypersurfaces (with L. Ambrozio and B. Sharp)
Calculus of Variations and PDE, 57 (2018), no. 1, 1-39.
A note on the index of closed minimal hypersurfaces of flat tori (with L. Ambrozio and B. Sharp)
Proceedings of the American Mathematical Society, 146 (2018), no. 1, pages 335-344.
Min-max embedded geodesic lines in asymptotically conical surfaces (with C. De Lellis)
Journal of Differential Geometry, 112 (2019), no. 3, pp. 411-445.
Index estimates for free boundary minimal hypersurfaces (with L. Ambrozio and B. Sharp)
Math. Ann., 370 (2018), no. 3-4, pages 1063-1078.
A non-existence result for minimal catenoids in asymptotically flat spaces (with A. Mondino)
Journal of the London Mathematical Society, 95 (2017), no. 2, pages 373-392.
Comparing the Morse index the first Betti number of minimal hypersurfaces (with L. Ambrozio and B. Sharp)
Journal of Differential Geometry, 108 (2018), no. 3, pages 379-410.
Effective versions of the positive mass theorem (with O. Chodosh and M. Eichmair)
Inventiones Mathematicae, 206 (2016), no. 3, pages 975-1016.
Generic finiteness of minimal surfaces with bounded Morse index
Ann. Scuola Norm. Sup. Pisa, XVII (2017), no. 3, pages 1153-1171.
Localizing solutions of the Einstein constraint equations (with R. Schoen)
Inventiones Mathematicae, 205 (2016), no. 3, pages 559-615.
Compactness of the space of minimal hypersurfaces with bounded volume and $p-$th Jacobi eigenvalue (with L. Ambrozio and B. Sharp)
Journal of Geometric Analysis, 26 (2016), no. 4, 2591-2601.
Minimal hyperspheres of arbitrarily large Morse index
Communications in Analysis and Geometry, 27 (2019), no. 5, 991-1023.
Rigidity of stable marginally outer trapped surfaces in initial data sets
Annales Henri Poincaré, 17 (2016), no. 10, 2421-2442.
Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
Calculus of Variations and PDE, 55 (2016), no. 3, 1-20.
Slowly converging Yamabe flows (with O. Chodosh and Y. Rubinstein)
Geometry & Topology, 19 (2015), 1523-1568.
Existence of generalized totally umbilic 2-spheres in perturbed 3-spheres (with A. Mondino)
International Mathematics Research Notices, 2014, no. 21, 6020-6052.
On the solvability of singular Liouville equations on compact surfaces of arbitrary genus
Transactions of the American Mathematical Society, 366 (2014), 1237-1256.
- Weighted barycentric sets and singular Liouville equation on compact surfaces (with A. Malchiodi)
Journal of Functional Analysis, 262 (2012), no. 2, 409-450.
Books and Research Monographs
Lectures on elliptic partial differential equations (with L. Ambrosio and A. Massaccesi)
in press, distributed by Springer in the SNS Lectures Notes series.
Surveys, reports, volume contributions
- Free boundary minimal surfaces: a survey of recent results
- Four lectures on asymptotically flat Riemannian manifolds
in Einstein equations: physical and mathematical aspects of general relativity, Birkhäuser (to appear).
- From scalar curvature rigidity phenomena to min-max geodesics
Oberwolfach Reports, 14 (2017), no. 3, 2268-2272.
- Effective index estimates via Euclidean isometric embeddings
Oberwolfach Reports, 13 (2016), no. 2, 1626-1629.
- Analyzing the rate of convergence of geometric flows
Oberwolfach Reports, 12 (2015), no. 3, 2078-2082.
- Localizing solutions of the Einstein constraint equations
Oberwolfach Reports, 11 (2014), no. 3, 1997-2000.
- Rigidity and flexibility phenomena in asymptotically flat spaces
Oberwolfach Reports, 11 (2014), no. 3, 1818-1822.
- A class of existence results for the singular Liouville equation (with A. Malchiodi)
Comptes Rendus de l'Acadèmie des Sciences, 349 (2011), no. 3-4, 161-166.
- Rigidity and flexibility phenomena in General Relativity
Stanford University Ph.D. Thesis (under the direction of Richard Schoen), 152 pages.
- A class of existence results for the singular Liouville equation
Università di Pisa Laurea Specialistica Thesis (under the direction of Andrea Malchiodi), 91 pages.
- A mass-transportation approach to some functional inequalities
Università di Pisa Laurea Thesis (under the direction of Luigi Ambrosio), 98 pages.