Stefano PIGOLA

Some recent papers

  • The Frankel property for self-shrinkers from the viewpoint of elliptic PDE's (joint with D. Impera and M. Rimoldi). Preliminary version
  • The smooth Riemannian extension problem. (Joint with G. Veronelli) Preliminary version
  • Nonlinear Calderón-Zygmund inequalities for maps (Joint with B. Güneysu). Ann. Glob. Anal. Geom. (to appear). Preliminary version
  • $L^p$ -interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatovic). (Joint with B. Güneysu). Ann. Mat. Pura Appl. (to appear). Preliminary version
  • Height estimates for Killing graphs. (Joint with D. Impera, J.H. de Lira, A.G. Setti). J. Geom. Anal. (to appear). Preliminary version
  • Sobolev spaces of maps and the Dirichlet problem for harmonic maps. (Joint with G. Veronelli). Comm. Contemp. Math (to appear). Preliminary version
  • Quantitative $C^1$-estimates on manifolds. (Joint with B. Güneysu). Int. Math. Res. Not. IMRN (to appear). Preliminary version
  • Potential theory on manifolds with boundary and applications to controlled mean curvature graphs. (Joint with D. Impera and A.G. Setti)  J. Reine Angew. Math. 733 (2017), 121-159. Preprint (see also
  • Hurewicz fibrations, almost submetries and critical points of smooth maps. (Joint with S.L. Cacciatori) Forum. Math. 29 (2017), 751-760. Preliminary version
  • Dirichlet parabolicity and $L^1$-Liouville property under localized geometric conditions. (Joint with L.F. Pessoa and A.G. Setti).  J. Funct. Anal. 273 (2017), 652-693. Preliminary version
  • On the growth of  supersolutions of nonlinear PDE's on exterior domains. (Joint with D. Impera)  Nonlinear Anal. 146 (2016), 20-31. Preprint
  • The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds. (Joint with B. Güneysu) Adv. Math. 281 (2015), 353-393. Preliminary version
  • Curvature estimates for submanifolds immersed in horoballs and horocylinders. (Joint with G.P. Bessa, J.H. Lira and A.G. Setti) J. Math. Anal. Appl. 431 (2015), 1000-1007. Preliminary version
  • On the Dirichlet problem for $p$-harmonic maps I: compact targets. (Joint with G. Veronelli). Geom. Dedicata 177 (2015), 307-322. Preprint
  • On the Dirichlet problem for $p$-harmonic maps II: targets with special structure. (Joint with G. Veronelli) To appear in Proc. Amer. Math. Soc. Preprint (see also
  • On submanifolds of highly negatively curved spaces. (Joint with G.P. Bessa and A.G. Setti) Internat. J. Math. 25 (2014), 1450055, 15 pages. Preliminary version
  • Complete self-shrinkers confined into some regions of the space. (Joint with M. Rimoldi) Annals Glob. Anal. Geom. 45 (2014), 47-65. Preliminary version
  • The connectivity at infinity of a manifold and $L^{q,p}$ Sobolev inequality. (Joint with A.G. Setti and M. Troyanov) Expositiones Math. 32 (2014),  365--383.
  • On the $L^1$-Liouville property of stochastically incomplete manifolds. (Joint with G.P. Bessa and A. G. Setti). Potential Analysis 39 (2013), 313-324. Preliminary version
  • Spectral and stochastic properties of the $f$-Laplacian, solutions of PDE's at infinity, and geometric applications. (Joint with G.P. Bessa and A.G. Setti) Revista Matematica Iberoamericana 29 (2013), 579–610. Preliminary version
  • Remarks on $L^p$-vanishing results in geometric analysis.  (Joint with G. Veronelli) Internat. J. Math.  23 (2012), 1250008, 18 pp. Preliminary version
  • The Feller property on Riemannian manifolds. (Joint with A.G. Setti) Jour. Funct. Anal. 262 (2012), 2481–2515. Preliminary version
  • Characterizations of model manifolds by means of certain differential systems. (Joint with M. Rimoldi) Canadian Math. Bull. 55 (2012), 632-645. Preliminary version
  • Uniform decay estimates for finite-energy solutions of semi-linear elliptic inequalities and geometric applications. (Joint with G. Veronelli) Diff. Geom. Appl. 29 (2011), 35-54. Preprint
  • Ricci almost solitons. (Joint with M. Rigoli, M. Rimoldi and A.G. Setti) To appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (2011), 757-799. Preliminary version
  • Lower volume estimates and Sobolev inequalities. (Joint with G. Veronelli) Proc. Amer. Math. Soc 138 (2010), 4479-4486. Preliminary (and expanded) version
  • Global comparison principles for the $p$-Laplace operator on Riemannian manifolds. (Joint with I. Holopainen and G. Veronelli) Potential Analysis 34 (2011), 371-384. Preliminary version
  • Remarks on non-compact gradient Ricci solitons. (Joint with M. Rimoldi and A.G. Setti) Math. Z. 268 (2011), 777-790. Preliminary version

My Ph.D. thesis
  • Maximum and comparison principles at infinity on complete manifolds. Advisor, Prof. Marco Rigoli. Pigola-thesis.pdf

Last updated 2018/05/23