Research

PUBLISHED AND ACCEPTED PAPERS

1. L. Mazzieri – Generalized connected sum construction for nonzero constant scalar curvature metrics (Communications in Partial Differential Equations, 33 (2008), Issue 1, pp. 1–17).

2. L. Mazzieri – Generalized connected sum construction for scalar flat metrics (Manuscripta Mathematica, 129 (2009), Issue 2, pp. 137–168).

3. L. Mazzieri – Generalized gluing for Einstein constraint equations (Calculus of Variations and Partial Differential Equations, 34 (2009), Issue 4, pp. 453–473).

4. G. Catino and L. Mazzieri – Connected sum construction for σk-Yamabe metrics (Journal of Geometric Analysis, 23 (2013), no.2, pp. 812–854).

5. G. Catino, C. Mantegazza, L. Mazzieri and M. Rimoldi – Locally conformally flat quasi-Einstein manifolds(Journal für die Reine und Angewandte Mathematik, 2013(2013), Issue 675, pp. 181–189).

6. L. Mazzieri and A. Segatti – Constant σk-curvature metrics with Delaunay type ends (Advances in Mathematics, 229 (2012), Issue 6, pp. 3147–3191).

7. G. Catino, C. Mantegazza and L. Mazzieri – On the global structure of conformal gradient solitons with nonnegative Ricci tensor (Communications in  Contemporary Mathematics, 14, 1250045 (2012)).

8. H.-D. Cao, G. Catino, Q. Chen, C. Mantegazza and L. Mazzieri – Bach flat gradient steady Ricci solitons (Calculus of Variations and Partial Differential Equations, 49 (2014), Issue 1-2, pp. 125–138).

9. E. Delay and L. Mazzieri – Refined gluing for Einstein constraint equations (Geometriae Dedicata, 173 (2014), Issue 1, pp. 393–415).

10. M. Gonzalez and L. Mazzieri – Singularities for a fully nonlinear elliptic equation in conformal geometry (Bulletin of the Institute of Mathematics Academia Sinica (New Series), special issue in honor of Prof. Neil Trudinger, 9 (2014), No. 2, pp. 223-244).

11. G. Catino, C. Mantegazza and L. Mazzieri – A note on Codazzi tensors (Mathematische Annalen, 362 (2015), Issue 1, pp. 629–638).

12. G. Catino, L. Mazzieri and S. Mongodi – Rigidity of gradient Einstein shrinkers (Communications in Contemporary Mathematics 17, 1550046 (2015)).

13. G. Catino, C. Mantegazza and L. Mazzieri – Locally conformally flat ancient Ricci flows (Analysis & PDE, 8 (2015), No. 2, pp. 365–371).

14. V. Agostiniani and L. Mazzieri – Riemannian aspects of potential theory (Journal de Mathématiques Pures et Appliquées, 104 (2015), Issue 3, pp. 561–586).

15. G. Catino and L. Mazzieri – Gradient Einstein solitons (Nonlinear Analysis, 132 (2016), pp. 66–94).

16. C. Arezzo, R. Lena and L. Mazzieri – On the resolution of extremal and constant scalar curvature Kähler orbifolds (International Mathematics Research Notices, Volume 2016 (2016), Number 21, pp. 6415–6452).

17. V. Agostiniani and L. Mazzieri – Comparing monotonicity formulas for electrostatic potentials and static metrics (Rendiconti Lincei. Matematica e Applicazioni, 28 (2017), pp. 7–20).

18. G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza and L. Mazzieri – The Ricci-Bourguignon flow (Pacific Journal of Mathematics 287-2 (2017), pp. 337–370).

19. V. Agostiniani and L. Mazzieri – On the geometry of the level sets of bounded static potentials (Communications in Mathematical Physics, v. 2017, (2017), pp. 261–301).

20. S. Borghini and L. Mazzieri – On the mass of static metrics with positive cosmological constant - I (Classical and Quantum Gravity 35 (2018)).

21. S. Borghini, G. Mascellani and L. Mazzieri – Some sphere theorems in linear potential theory (Transactions of the American Mathematical Society, 371 (2019), pp. 7757–7790).

22. M. Fogagnolo, L. Mazzieri and A. Pinamonti – Geometric aspects of p-capacitary potentials (Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, Volume 36, Issue 4, July 2019, pp. 1151–1179).

23. C. Arezzo, A. Della Vedova, R. Lena and L. Mazzieri – On the Kummer construction for Kcsc metrics (Bollettino dell'Unione Matematica Italiana, 12, (2019), pp. 12–83).

24. S. Borghini and L. Mazzieri – Monotonicity formulas for static metrics with non-zero cosmological constant (Springer-Indam, volume 33 (2019), ”Contemporary Research in Elliptic PDEs and Related Topics”, pp. 129–202).

25. V. Agostiniani and L. Mazzieri – Monotonicity formulas in potential theory (Calculus of Variations and Partial Differential Equations, 59 (2020), Issue 6). 

26. S. Borghini and L. Mazzieri – On the mass of static metrics with positive cosmological constant - II (Communications in Mathematical Physics, 377, 2079–2158 (2020)). 

27. V. Agostiniani, M. Fogagnolo and L. Mazzieri – Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature (Inventiones mathematicae, 222, (2020), pp. 1033–1101).

28. V. Agostiniani, L. Mazzieri and F. Oronzio – A geometric capacitary inequality for sub-static manifolds with harmonic potentials (Mathematics in Engineering, 4(2), (2021), pp. 1-40).

29. M. Fogagnolo and L. Mazzieri – Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds (Journal of Functional Analysis, Volume 283, Issue 9, 1 November 2022).

30. V. Agostiniani, M. Fogagnolo and L. Mazzieri – Minkowski inequalities via nonlinear potential theory (Archive for Rational Mechanics and Analysis, 244, (2022), pp. 51–85).

31. L. Benatti, M. Fogagnolo and L. Mazzieri – The asymptotic behaviour of p-capacitary potentials in asymptotically conical manifolds (Mathematische Annalen, (2022)).

32. M. Fogagnolo, A. Malchiodi and L. Mazzieri – A note on the critical Laplace equation and Ricci curvature (To appear on The Journal of Geometric Analysis, (2023)).

33. S. Borghini, P. T. Chruściel and L. Mazzieri – On the uniqueness of Schwarzschild-de Sitter spacetime (To appear on Archive for Rational Mechanics and Analysis, (2023)).

34. S. Borghini and L. Mazzieri – Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields (To appear on Annals of Global Analysis and Geometry, (2023)).

35. L. Benatti, M. Fogagnolo and L. Mazzieri – Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature (To appear on Analysis and PDE's, (2023)).

36. V. Agostiniani, S. Borghini and L. Mazzieri – On the Serrin problem for ring-shaped domains (To appear on J. Eur. Math. Soc., (2023)).

PREPRINTS

1. L. Benatti, M. Fogagnolo and L. Mazzieri – Nonlinear isocapacitary concepts od mass in nonnegative scalar curvature (Preprint-2023).

2. L. Benatti, M. Fogagnolo and L. Mazzieri – On the Isoperimetric Riemannian Penrose inequality (Preprint-2022).

3. V. Agostiniani, C. Mantegazza, L. Mazzieri and F. Oronzio – Riemannian Penrose inequality via Nonlinear Potential Theory (Preprint-2022).

4. V. Agostiniani, L. Mazzieri and F. Oronzio – A Green’s function proof of the Positive Mass Theorem (Preprint-2021).

5. C. Arezzo, A. Della Vedova and L. Mazzieri – K-stability, Futaki invariants and cscK metrics on orbifold resolutions (Preprint-2018).