In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the...In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].展开更多
If the geometrical system of units c = G 1 and the Planck length as a natural length scale are used in the construction of the Penrose space (diagram) corresponding to Minkowski spacetime, the presence of the Planck c...If the geometrical system of units c = G 1 and the Planck length as a natural length scale are used in the construction of the Penrose space (diagram) corresponding to Minkowski spacetime, the presence of the Planck constant ħin the Penrose dimensionless time (ζ) and radial (ρ) coordinates is unavoidable. This fact suggests that there could be a deep and still unknown relation between the spacetime of special relativity and quantum mechanics.展开更多
基金Supported by National Natural Science Foundation of China(12171260).
文摘In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].
文摘If the geometrical system of units c = G 1 and the Planck length as a natural length scale are used in the construction of the Penrose space (diagram) corresponding to Minkowski spacetime, the presence of the Planck constant ħin the Penrose dimensionless time (ζ) and radial (ρ) coordinates is unavoidable. This fact suggests that there could be a deep and still unknown relation between the spacetime of special relativity and quantum mechanics.
