In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece...In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.展开更多
The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and ide...The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.展开更多
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.
文摘The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.
