Publications


  • Existence and Uniqueness of Green functions for the Cheeger p-Laplacian in PI spaces, (joint with M. Bonk and L. Capogna), arXiv.

  • A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces, (joint with P. Lahti and A. Pinamonti), arXiv.

  • Horizontally quasiconvex envelope in the Heisenberg group, (joint with A. Kijowski and Q. Liu), arXiv

  • Absolutely continuous mappings on doubling metric measure spaces, (joint with P. Lahti), submitted, arXiv

  • Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces, (joint with P. Lahti), submitted, arXiv

  • Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces, (joint with P. Lahti), submitted, arXiv

  • Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces, (with Q. Liu), accepted by Minimax Theory and its Applications.

  • Equivalence of solutions of eikonal equation in metric spaces, (joint with Q. Liu and N. Shanmugalingam), J. Differential Equations 272 (2021), 979–1014. arXiv

  • Functions of bounded variation on complete and connected one-dimensional metric spaces, (with P. Lahti), Int. Math. Res. Not. IMRN 2021, no. 20, 15412–15443.  arXiv

  • Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations, (with Q. Liu),  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 4, 2039–2076. arXiv

  • Absolutely continuous functions on compact and connected one-dimensional metric spaces, Ann. Acad. Sci. Fenn. Math. Volumen 44, (2019), 281-291.
     PDF file

  • Strong comparison principle for p-harmonic functions in Carnot-Caratheodory spaces, (with L. Capogna), Proc. Amer. Math. Soc. 146 (2018)no. 10, 4265-4274.  arXiv

  • Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group, (with Q. Liu), Nonlinear Anal. 174 (2018), 54-78. PDF file

  • Sobolev functions in the critical case are uniformly continuous in s-Ahlfors regular metric spaces when s less than or equal to one, Proc. Amer. Math. Soc. 145 (2017), no. 1, 267-272. arXiv

  • Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group, (with Q. Liu and J. J. Manfredi), Calc. Var. Partial Differential Equations 55 (2016), no.4, Art. 80, 25pp. arXiv

  • Sobolev embedding on a sphere containing an arbitrary Cantor set in the image, (with P. Hajlasz), Geom. Dedicata. 184 (2016), 159--173. arXiv

  • A game-theoretic proof of convexity preserving properties for motion by curvature, (with Q. Liu and A. Schikorra), Indiana Univ. Math. J. 65 (2016), 171--197. PDF file