I am a mathematical research fellow at SISSA, Trieste, Italy.
Before that I got my first Ph.D. from Beihang University, China, supervised by Yuan Zhou in 2023, focusing on various topics of calculus of variation. And I got my second Ph.D. from University of Jyväskylä, Finland, supervised by Katrin Fässler and Tuomas Orponen in 2024, focusing on geometric measure theory.
jliu@sissa.it
Calculus of Variation and Geometric Analysis;
Geometric Measure Theory;
N-body Problem
One Dimensional Asymptotic Plateau Problem in n-Dimensional Asymptotically Conical Manifolds (joint with Shijin Zhang and Yuan Zhou) (Arxiv)
Restricted Projections to Lines in R^{n+1}. Mathematical Proceedings of the Cambridge Philosophical Society (2025), 179, 105–143 (Journal) (Arxiv)
On the Hausdorff dimension of circular Furstenberg sets (joint with Katrin Fässler and Tuomas Orponen). Discrete Analysis, December, 2024 (Journal)
A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition (joint with Shijin Zhang and Yuan Zhou) Journal of Functional Analysis, Volume 286, Issue 10, 2024 (Journal) (Arxiv)
HW^{2,2}_loc regularity for p-harmonic functions in Heisenberg groups (joint with Fa Peng and Yuan Zhou). Advances in Calculus of Variations, vol. 16, no. 2, 2023 (Journal) (Arxiv)
Existence of hyperbolic motions to a class of Hamiltonians and generalized N-body system via a geometric approach (joint with Duokui Yan and Yuan Zhou) Archive for Rational Mechanics and Analysis, 247, Article 64, 2023 (Journal) (Arxiv)
A Rademacher type theorem for Hamiltonians H(x,p) and application to absolute minimizers (joint with Yuan Zhou). Calculus of Variations and Partial Differential Equations, 62, Article 144, 2023 (Journal) (Arxiv)
Dimension Estimates on Circular (s,t)-Furstenberg Sets. Annales Fennici Mathematici, 48(1), 2023 (Journal) (Arxiv)
On the Dimension of Kakeya Sets in the First Heisenberg Group. Proceedings of the American Mathematical Society, 150(8), 2022 (Journal) (Arxiv)