9 citations · 20 across the 13 of their papers we have counts for
13 papers
Non-quadratic Euclidean complete affine maximal type hypersurfaces for
Shi-Zhong Du
Bernstein problem for affine maximal type equation \begin{equation}\label{e0.1} u^{ij}D_{ij}w=0, \ \ w\equiv[\det D^2u]^{-θ},\ \ \forall x\inΩ\subset{\mathbb{R}}^N \end{equation} h…
On the planar Lp-Minkowski problem
Shi-Zhong Du
In this paper, we study the planar Lp-Minkowski problem for all p, which was introduced by Lutwak [23]. A detailed exploration on solvability and uniqueness will be presented.
Sufficient and Necessary Condition of the Lp-Brunn-Minkowski Inequality Conjecture for p\in[0,1)
Shi-Zhong Du
The Lp-Brunn-Minkowski inequality palys a central role in the Brunn-Minkowski theory proposed by Firey [13] in 60's and developed by Lutwak [26,27] in 90's, which generalizes the c…
Necessary and Sufficient Conditions to Bernstein Theorem of a Hessian Equation
Shi-Zhong Du
The Hessian quotient equatio were studied for k-th symmetric elementary function S_k(D^2u) of eigenvalues of the Hessian matrix D^2u. Two pointwise quadratic growth conditions were…
Complete Classification of the Euclidean Complete Solutions to a Monge-Ampere Equation
Shi-Zhong Du, Chen-Long Wu, Fei-Hao Zheng
We study a Monge-Ampère equation with power term for some . A solution is called to be Euclidean complete if it is an entire solution defined over the whole $…
Nonuniqueness and nonexistence results for the Lp-dual Minkowski problem with supercritical exponents
Shi-Zhong Du, YanNan Liu, Jian Lu
In this paper, the -dual Minkowski problem of Monge-Ampère type were studied for different and . Some new nonuniqueness results we…
Finite time blowup and type II rate for harmonic heat flow from Riemannian manifolds
Shi-Zhong Du
In this paper, we will study the existence of finite time singularity to harmonic heat flow and their formation patterns. After works of Coron-Ghidaglia, Ding and Chen-Ding, one kn…
Bernstein Problem of Affine Maximal Type Hypersurfaces on Dimension N>=3
Shi-Zhong Du
Bernstein problem for affine maximal type equation has been a core problem in affine geometry. A conjecture proposed firstly by Chern for entire graph and then extended by Trudinge…
Zero Comparison Theorem of Sturm-Liouville Type for Harmonic Heat Flow
Shi-Zhong Du
In this paper, we will prove a zero comparison theorem of Sturm-Liouville type for linearized harmonic heat flow for rotational symmetric solutions.
Energy Non-collapsing and Refined Blowup for a Semilinear Heat Equation
Shi-Zhong Du
Refined structures of blowup for non-collapsing maximal solution to a semilinear parabolic equation are studied. We will prove that the blowup set is empty for non-collapsing blowi…
An existence and uniqueness result for orientation-reversing harmonic diffeomorphism from to
Shi-Zhong Du, Xu-Qian Fan
In this paper, we prove an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms from to with rotational symmetry, w…
A nonexistence result on harmonic diffeomorphisms between punctured spaces
Shi-Zhong Du, Xu-Qian Fan
In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of…
Rotationally symmetric harmonic diffeomorphisms between surfaces
Li Chen, Shi-Zhong Du, Xu-Qian Fan
In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric…