arXiv subjects
Publications and source records attributed to Qing Han.
We study the asymptotic behaviors of solutions of the Loewner-Nirenberg problem in singular domains and prove that the solutions are well approximated by the corresponding solutions in tangent cones at singular points on the boundary. The conformal structure of the underlying equation plays an essential role in the derivation of the optimal estimates.
In the Cloud Radio Access Network (C-RAN) architecture, a Control Unit (CU) implements the baseband processing functionalities of a cluster of Base Stations (BSs), which are connected to it through a fronthaul network. This architecture enables centralized processing at the CU, and hence the implementation of enhanced interference mitigation strategies, but it also entails an increased decoding latency due to the transport on the fronthaul network. The fronthaul latency may offset the benefits of centralized processing when considering the performance of protocols at layer 2 and above. This letter studies the impact of fronthaul latency on the performance of standard Automatic Retransmission reQuest (ARQ) protocols, namely Stop and Wait, Go-Back-N and Selective Repeat. The performance of the C-RAN architecture in terms of throughput and efficiency is compared to the that of a conventional cellular system with local processing, as well as with that of a proposed hybrid C-RAN system in which BSs can perform decoding. The dynamics of the system are modeled as a multi-dimensional Markov process that includes sub-chains to capture the temporal correlation of interference and channel gains. Numerical results yield insights into the impact of system parameters such as fronthaul latency and signal-to-interference ratio on different ARQ protocols.
In this paper, we study the existence of smooth local solutions to Weingarten equations and $σ_k$-equations. We will prove that, for $2 \leq k \leq n$, the Weingarten equations and the $σ_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately.
We study a class of compact surfaces in $\mathbb R^3$ introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures.
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.
Mahler's PHD (Probability Hypothesis Density) filter and its particle implementation (as called the particle PHD filter) have gained popularity to solve general MTT (Multi-target Tracking) problems. However, the resampling procedure used in the particle PHD filter can cause sample impoverishment. To rejuvenate the diversity of particles, two easy-to-implement roughening approaches are presented to enhance the particle PHD filter. One termed as "separate-roughening" is inspired by Gordon's roughening procedure that is applied on the resampled particles. Another termed as "direct-roughening" is implemented by increasing the simulation noise of the state propagation of particles. Four proposals are presented to customize the roughening approach. Simulations are presented showing that the roughening approach can benefit the particle PHD filter, especially when the sample size is small.
We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.
We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.
We prove the existence of C^{\infty} local solutions to a class of mixed type Monge-Ampere equations in the plane. More precisely, the equation changes type to finite order across two smooth curves intersecting transversely at a point. Existence of C^{\infty} global solutions to a corresponding class of linear mixed type equations is also established. These results are motivated by, and may be applied to the problem of prescribed Gaussian curvature for graphs, the isometric embedding problem for 2-dimensional Riemannian manifolds into Euclidean 3-space, and also transonic fluid flow.
In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension greater than 4. This is accomplished by introducing a smaller yet equivalent linearized system, in an appropriate way, which facilitates analysis of the characteristic variety.
Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion.
We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves intersecting transversely at a point, then local sufficiently smooth isometric embeddings exist.
We prove that any homogeneous order one solution to 3-d nondivergence elliptic equations must be linear.