arXiv subjects

Zhifei Zhu

Publications and source records attributed to Zhifei Zhu.

9 recordsLinked to original sources

arXiv2026

Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters

We prove sharp $k$-linear $L^p$ estimates for Carleson--Sjölin oscillatory integral operators with arbitrary separated frequency scales for all $k\ge 2$ and $1\le p\le \infty$. The estimates are sharp, including the endpoint logarithmic behavior for general Carleson--Sjölin phases. Moreover, we obtain log-free endpoint bilinear spectral cluster estimates on every closed three-dimensional Riemannian manifold, resolving a problem of Burq--Gérard--Tzvetkov. As a consequence, we establish sharp $k$-linear $L^p$ spectral cluster estimates for all $k\ge 2$ and $1\le p\le \infty$.

math.AP↗

arXiv2026

Restriction estimates for toral eigenfunctions and lattice points in spherical regions

We establish new $L^2$ restriction estimates for toral eigenfunctions. These estimates are sharp in certain cases, and thus prove a conjecture of Huang-Zhang for smooth submanifolds of large codimension. In particular, they provide new progress toward a conjecture of Bourgain-Rudnick. The proof combines a slicing and packing method with the approximation of the discrete spherical multiplier by Magyar-Stein-Wainger and Magyar.

math.AP↗

arXiv2026

Maximal growth of the Stein-Wainger oscillatory integral

We establish a precise hierarchy for the maximal growth of the Stein-Wainger oscillatory integral as the regularity of the phase varies over Denjoy-Carleman classes, such as the Gevrey classes and their generalizations. In particular, we resolve a problem posed by Wang--Zhang, motivated by eigenfunction restriction estimates on curves, and also provide a new proof of a theorem of Nagel--Wainger on the Hilbert transform along curves. A key ingredient is the sharp estimate on the growth of a phase near a flat point.

math.CA↗

arXiv2026

Homological Filling and Minimal Varifolds in Four-Dimensional Einstein Manifolds

We study the smallest area $A(M,g)$ of a 2-dimensional stationary integral varifold in a closed Einstein 4-manifold $(M^4,g)$ with $Ric_g = λg, |λ|\leq 3, Vol(M,g)\geq v>0, diam(M,g)\leq D, H_1(M;\mathbb{Z})=0.$ Building on the previous work on homological filling functions, we show that for every $(M^4,g)$ in this Einstein class, there is an upper bound $A(M,g)\leq F_{Ein}(v,D),$ where $F_{Ein}$ depends only on $(v,D)$ and on quantitative Sobolev and $\varepsilon$-regularity constants for Einstein metrics.

math.DG↗

arXiv2024

Length of closed geodesics on Riemannian manifolds with good covers

In this article, we prove a generalization of our previous result in [12]. In particular, we show that for an $n$-dimensional, simply connected Riemannian manifold with diameter $D$ and volume $V$. Suppose that $M$ admits a good cover consisting of $N$ elements. Then, the length of a shortest closed geodesic on $M$ is bounded by some function that only depends on $V, D$, and $N$.

math.DG↗

arXiv2023

Large nonlinear Hall effect and Berry curvature in KTaO3 based two-dimensional electron gas

The two-dimensional electron gas (2DEG) at oxide interfaces exhibits various exotic properties stemming from interfacial inversion symmetry breaking. In this work, we report the emergence of large nonlinear Hall effects (NHE) in the LaAlO3/KTaO3(111) interface 2DEG under zero magnetic field. Skew scattering was identified as the dominant origin based on the cubic scaling of nonlinear Hall conductivity with longitudinal conductivity and the threefold symmetry. Moreover, a gate-tunable NHE with pronounced peak and dip was observed and reproduced by our theoretical calculation. These results indicate the presence of Berry curvature hotspots and thus a large Berry curvature triple at the oxide interface. Our theoretical calculations confirm the existence of large Berry curvatures from the avoided crossing of multiple 5d-orbit bands, orders of magnitude larger than that in transition-metal dichalcogenides. NHE offers a new pathway to probe the Berry curvature at oxide interfaces, and facilitates new applications in oxide nonlinear electronics.

cond-mat.mtrl-sci↗

arXiv2018

Length of a shortest closed geodesic in manifolds of dimension four

In this paper, we show that for any closed 4-dimensional simply-connected Riemannian manifold $M$ with Ricci curvature $|Ric|\leq 3$, volume $vol(M)>v>0$, and diameter $diam(M)<D$, the length of a shortest closed geodesic is bounded by a function $F(v,D)$ which only depends on $v$ and $D$. The proofs of our result are based on a recent theorem of diffeomorphism finiteness of the manifolds satisfying the above conditions proven by J. Cheeger and A. Naber.

math.DG↗

arXiv2017

An upper bound for the smallest area of a minimal surface in manifolds of dimension four

In this paper, we prove that for any closed 4-dimensional Riemannian manifold $M$ with trivial first homology group, if the Ricci curvature $|Ric|\leq3$, the diameter $diam(M)\leq D$ and the volume $vol(M)>v>0$, then the area of a smallest 2-dimensional stationary integral varifold in $M$ is bounded by F(v,D), for some function F that only depends on v and D. Our bound for the area is based on the estimation of the first homological filling function of $M$.

math.DG↗

arXiv2016

Subdividing Three-Dimensional Riemannian Disks

P. Papasoglu asked in [Pap13] whether for any Riemannian 3-disk $M$ with diameter $d$, boundary area $A$ and volume $V$, there exists a homotopy $S_t$ contracting the boundary to a point so that the area of $S_t$ is bounded by $f(d,A,V)$ for some function $f$. He further asks whether it is possible to subdivide $M$ by a disk $D$ into two regions of volume $V/4$ so that the area of $D$ is bounded by some function $h(d,A,V)$. In this paper, we answer the questions above in the negative. We further prove that given $N>0$ and $c\in(0,1)$, one can construct a metric $g'$ so that any 2-disk $D$ subdividing $(M,g')$ into two regions of volume at least $cV$, the area of $D$ is greater than $N$. We also prove that for any Riemannian 3-sphere $M$, there is a surface that subdivides the disk into two regions of volume no less than $V/6$, and the area of this surface is bounded by $3\operatorname{HF}_1(2d)$, where $\operatorname{HF}_1$ is the homological filling function of $M$.

math.DG↗