arXiv subjects
Publications and source records attributed to Zhijie Huang.
Based on the work of Schoen-Yau, we derive an estimate of the first eigenvalue of a Schrödinger Operator (the Jaocbi operator of minimal surfaces in flat 3-spaces) on surfaces.
Let $(M,g,ϕ)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $ϕ$. We show that a complete, $κ$-noncollapsed solution $(M,g,ϕ)$ to this coupled Ricci flow with a Type I singularity at time $T<\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow.
Entangled pseudoscalar neutral meson pairs have been used in studying CP violation and searching CPT violation, but almost all the previous works concern $C=-1$ entangled state. Here we consider $C=+1$ entangled state of pseudoscalar neutral mesons, which is quite different from $C=-1$ entangled state and provides complementary information on symmetry violating parameters. After developing a general formalism, we consider three kinds of decay processes, namely, semileptonic-semileptonic, hadronic-hadronic and semileptonic-hadronic processes. For each kind of processes, we calculate the integrated rates of joint decays with a fixed time interval, as well as asymmetries defined for these joint rates of different channels. In turn, these asymmetries can be used to determine the four real numbers of the two indirect symmetry violating parameters, based on a general relation between the symmetry violating parameters and the decay asymmetries presented here. Various discussions are made on indirect and direct violations and the violation of $Δ{\cal F} =ΔQ$ rule, with some results presented as theorems.
We present a general model-independent formalism of measuring CP and CPT violating parameters through time-ordered integrated rates of correlated decays of $C=\pm 1$ entangled states of neutral pseudoscalar mesons. We give the general formulae of CP and CPT violating parameters in terms of four measurable asymmetries defined for the time-ordered integrated rates, applicable to all kinds of decay product. Two special cases which are often realized in experiments are discussed specifically.
In this paper we study gradient estimates for the positive solutions of the porous medium equation: $$u_t=Δu^m$$ where $m>1$, which is a nonlinear version of the heat equation. We derive local gradient estimates of the Li-Yau type for positive solutions of porous medium equations on Riemannian manifolds with Ricci curvature bounded from below. As applications, several parabolic Harnack inequalities are obtained. In particular, our results improve the ones of Lu, Ni, Vázquez and Villani in [10]. Moreover, our results recover the ones of Davies in [4], Hamilton in [5] and Li and Xu in [7].