I am a doctoral student in Department of Mathematics and Statistics at University of Jyväskylä, Finland supervised by Katrin Fässler and Tuomas Orponen.

I also hold a Ph.D. from Beihang University, China supervised by Yuan Zhou.  

Email:

jiayin.mat.liu@jyu.fi

Research Interests

• N-body Problem; 

• Geometric PDEs and Calculus of Variation; 

• Geometric Measure Theory

Publications & Preprints

1. Restricted Projections to Lines in R^{n+1}. https://arxiv.org/abs/2312.04453 

2. On the Hausdorff dimension of circular Furstenberg sets (joint with Katrin Fässler and Tuomas Orponen). https://arxiv.org/abs/2305.11587

3. 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 https://arxiv.org/abs/2205.10503

4. Dimension Estimates on Circular (s,t)-Furstenberg Sets. Annales Fennici Mathematici, 48(1), 2023  https://arxiv.org/abs/2204.01770           

5. 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 https://arxiv.org/abs/2112.07908 

6. 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 https://arxiv.org/abs/2112.07470 

7. 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 https://arxiv.org/abs/2112.07450 

8. On the Dimension of Kakeya Sets in the First Heisenberg Group. Proceedings of the American Mathematical Society, 150(8), 2022 https://arxiv.org/abs/2106.11937