List of publications

Research Articles

• Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group (with D. Wiygul and M. Schulz)
  submitted.

• Minimal hypertori in the four-dimensional sphere (with M. Schulz)
  submitted.

• Constrained deformations of positive scalar curvature metrics, II (with C. Li)
  Communications on Pure and Applied Mathematics, to appear, 75 pp.

• Free boundary minimal surfaces with connected boundary and arbitrary genus (with G. Franz and M. Schulz)
  Cambridge Journal of Mathematics, 10 (2022), no. 4, 835-857.

  Gallery of free boundary minimal surfaces with connected boundary:

  genus one - genus two - genus three - genus five

  genus two (3d dynamic visualisation)

• Contractibility results for certain spaces of Riemannian metrics on the disc (with D. Wu)
  Mathematical Research Letters, 28 (2021), no. 4, 1033-1045.

• Inequivalent complexity criteria for free boundary minimal surfaces (with G. Franz)
  Advances in Mathematics, 373 (2020), 107322, 68 pp.

• Constrained deformations of positive scalar curvature metrics (with C. Li)
  Journal of Differential Geometry, to appear, 80 pp.

• 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)
  Calculus of Variations and PDE, to appear, 16 pp.

• 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

• The general relativistic constraint equations
  distributed by SpringerNature in the series Living Reviews in Relativity, 2021, volume 24:2, 170 pp.

• Lectures on elliptic partial differential equations (with L. Ambrosio and A. Massaccesi)
  distributed by Springer in the series Lecture Notes. Scuola Normale Superiore di Pisa (New Series), 18. Edizioni della Normale, Pisa, 2018. x+227 pp.

  Here you find the front cover, the table of contents and the index

  Here you find the Mathscinet Review of the book

Surveys, reports, volume contributions

• A survey on positive scalar curvature metrics
  Boll. Unione Matematica Italiana, 14 (2021), no. 1, 17-42.

  Invited contribution to a special volume on the occasion of the special volume of XXI congress of the Unione Matematica Italiana.

• Free boundary minimal surfaces: a survey of recent results
  Rend. Accad. Sci. Fis. Mat. Napoli (4), 86 (2019), 103-123.

  Invited contribution on the occasion of the conferral of the Riccardo De Arcangelis Prize.

• Four lectures on asymptotically flat Riemannian manifolds
  in Einstein equations: physical and mathematical aspects of general relativity, distributed by Springer in the series Tutorials, Schools and Workshops in the Mathematical Sciences, Birkhäuser, Basel, 2019, xiv+357 pp.

• 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.

Theses

• 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.