Jiayin Liu

most citedOn the Dimension of Kakeya Sets in the First Heisenberg Group

4 citations · 4 across the 5 of their papers we have counts for

collaborators

5 papers

math.CA2022

A Rademacher type theorem for Hamiltonians $H (x, p)$ and application to absolute minimizers

Jiayin Liu, Yuan Zhou

We establish a Rademacher type theorem involving Hamiltonians $H (x, p)$ under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular, $H (x, p)$ is ass…

math.AP2021

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

Jiayin Liu, Fa Peng, Yuan Zhou

Let $1 < p \leq 4$ when $n = 1$ and $1 < p < 3 + \frac{1}{n - 1}$ when $n \geq 2$ . We obtain the second-order horizontal Sobolev $H W_{loc}^{2, 2}$ -regularity of $p$ -harmonic functions in the H…

math.AP2021

A quantitative second order estimate for (weighted) $p$ -harmonic functions in manifolds under curvature-dimension condition

Jiayin Liu, Shijin Zhang, Yuan Zhou

We build up a quantitative second order Sobolev estimate of $ln w$ for positive $p$ -harmonic functions $w$ in Riemannian manifolds under Ricci curvature bounded from blow and als…

math.DS2021

Existence of hyperbolic motions to a class of Hamiltonians and generalized $N$ -body system via a geometric approach

Jiayin Liu, Duokui Yan, Yuan Zhou

For the classical $N$ -body problem in $R^{d}$ with $d \geq 2$ , Maderna-Venturelli in their remarkable paper [Ann. Math. 2020] proved the existence of hyperbolic motions with an…

math.CA2021★ 4 cited

On the Dimension of Kakeya Sets in the First Heisenberg Group

Jiayin Liu

We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp…

A Rademacher type theorem for Hamiltonians H(x,p) and application to absolute minimizers

HWloc2,2​-regularity for p-harmonic functions in Heisenberg groups

A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition

Existence of hyperbolic motions to a class of Hamiltonians and generalized N-body system via a geometric approach

On the Dimension of Kakeya Sets in the First Heisenberg Group

A Rademacher type theorem for Hamiltonians $H (x, p)$ and application to absolute minimizers

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

A quantitative second order estimate for (weighted) $p$ -harmonic functions in manifolds under curvature-dimension condition

Existence of hyperbolic motions to a class of Hamiltonians and generalized $N$ -body system via a geometric approach