Papers
- S. Honda, L. Mari, M. Rimoldi, G. Veronelli Density and non-density of C_{c}^{∞}↪W^{k,p} on complete manifolds with curvature bounds.
Nonlinear Analysis. 211 (2021), 112429. doi: 10.1016/j.na.2021.112429 - D. Impera, M. Rimoldi, G. Veronelli Higher order distance-like functions and Sobolev spaces.
Advances in Mathematics. 396 (2022), 108166. doi: 10.1016/j.aim.2021.108166 - D. Impera, S. Pigola, M. Rimoldi The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's.
Journal für die reine und angewandte Mathematik. 773 (2021), 1–20. doi: 10.1515/crelle-2020-0044 - D. Impera, M. Rimoldi Index and first Betti number of f-minimal hypersurfaces: general ambients.
Annali di Matematica Pura ed Applicata. 199 (2020), no. 6, 2151–2165. doi: 10.1007/s10231-020-00961-y - D. Impera, M. Rimoldi, G. Veronelli Density problems for second order Sobolev spaces and cut-off functions on manifolds with unbounded geometry.
International Mathematics Research Notices (2021), no. 14, 10521-10558. doi:10.1093/imrn/rnz131 - M. Rimoldi, G. Veronelli Extremals of Log Sobolev inequality on non-compact manifolds and Ricci soliton structures.
Calculus of Variations and Partial Differential Equations. (2019), 58:66 doi: 10.1007/s00526-019-1518-z - D. Impera, M. Rimoldi Quantitative index bounds for translators via topology.
Mathematische Zeitschrift. 292 (2019), no. 1-2, 513-527, doi: 10.1007/s00209-019-02276-y - D. Impera, M. Rimoldi, A. Savo Index and first Betti number of f-minimal hypersurfaces and self-shrinkers.
Revista Matematica Iberoamericana. 36 (2020), no. 3, 817–840.. doi:10.4171/rmi/1150 - C. Mantegazza, S. Mongodi, M. Rimoldi, The Cotton tensor and the Ricci flow.
Geometric Flows 2 (2017), 49-71, doi: 10.1515/geofl-2017-0001. - D. Impera, M. Rimoldi, Rigidity results and topology at infinity of translating solitons of the mean curvature flow.
Communications in Contemporary Mathematics. 19 (2017), no. 6, 1750002, 21 pp., doi: 10.1142/S021919971750002X - D. Impera, M. Rimoldi, Stability properties and topology at infinity of f-minimal hypersurfaces.
Geometriae Dedicata. 178 (2015), no. 1, 21-47, doi: 10.1007/s10711-014-9999-6 - M. Rimoldi, G. Veronelli, Topology of steady and expanding gradient Ricci solitons via f-harmonic maps.
Differential Geometry and its Applications. 31 (2013), no. 5, 623-638, doi: 10.1016/j.difgeo.2013.06.001. - S. Pigola, M. Rimoldi, Complete self-shrinkers confined into some regions of the space.
Annals of Global Analysis and Geometry. 45 (2014), no. 1, 47-65, doi: 10.1007/s10455-013-9387-8. - P. Mastrolia, M. Rimoldi, Some triviality results for quasi-Einstein manifolds and Einstein warped products.
Geometriae Dedicata. 169 (2014), no. 1, 225-237, doi: 10.1007/s10711-013-9852-3. - M. Rimoldi, On a classification theorem for self-shrinkers.
Proceedings of the American Mathematical Society. 142 (2014), no. 10, 3605-3613, doi:10.1090/S0002-9939-2014-12074-0. - P. Mastrolia, M. Rigoli, M. Rimoldi, Some geometric analysis on generic Ricci solitons.
Communications in Contemporary Mathematics. 15 (2013), no.3, 1250058, 25 pp., doi: 10.1142/S0219199712500587. - G. Catino, C. Mantegazza, L. Mazzieri, M. Rimoldi, Locally conformally flat quasi-Einstein manifolds.
Journal für die reine und angewandte Mathematik 675 (2013), 181-189, doi: 10.1515/crelle.2011.183. - M. Rimoldi, A remark on Einstein warped products.
Pacific Journal of Mathematics 252 (2011), no. 1, 207-218, doi: 10.2140/pjm.2011.252.207. - P. Mastrolia, M. Rimoldi, G. Veronelli, Myers-type theorems and some related oscillation results.
Journal of Geometric Analysis 22 (2012), no. 3, 763-779, doi: 10.1007/s12220-011-9213-0. - S. Pigola, M. Rigoli, M. Rimoldi, A. G. Setti, Ricci almost solitons.
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze X (2011), no. 4, 757-799, doi: 10.2422/2036-2145.2011.4.01. - S. Pigola, M. Rimoldi, A. G. Setti, Remarks on non-compact gradient Ricci solitons.
Mathematische Zeitschrift 268 (2011), no. 3-4, 777-790, doi: 10.1007/s00209-010-0695-4. - S. Pigola, M. Rimoldi, Characterizations of model manifolds by means of certain differential systems.
Canadian Mathematical Bulletin 55 (2012), 632-645, doi:10.4153/CMB-2011-134-0.
Preprints
- D. Impera, N. M. Møller, M. Rimoldi Rigidity and non-existence results for collapsed translators. Preprint
Thesis
- Ph.D. Thesis, Rigidity results for Lichnerowicz Bakry-Emery Ricci tensors. Advisor: Prof. Stefano Pigola.
- Master Thesis, Caratterizzazione di modelli mediante equazioni differenziali. (Italian) Advisor: Prof. Stefano Pigola.
Some slides
- Extremals of Log Sobolev inequality on non-compact manifolds and Ricci soliton structures.
- Properness and boundedness properties of complete self-shrinkers for the mean curvature flow.
- Rigidity results for Lichnerowicz Bakry-Emery Ricci tensors.
- Triviality results for quasi-Einstein metrics and Einstein warped products.