We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [M...We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.展开更多
Let f be a smooth strictly convex solution ofdefined on a domain Ω C R^n, where ai, bi and c are constants. Then the graph Mvf of △f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean spa...Let f be a smooth strictly convex solution ofdefined on a domain Ω C R^n, where ai, bi and c are constants. Then the graph Mvf of △f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space with the translating vector（al, a2, . ., an; bz, b2, , bn）. In this paper, we will use alCfine technique to show a Berustein Theorem： if the graph Mvf is complete, then f（x） must be a quadratic polynomial and Mvf is an ailine n-plane.展开更多
In this paper, some results about approximation in a norm S induced by the minimax series are studied. Then a Bernstein-type theorem for the norm S is established. Finally the Bernstein theorem is applied to prove the...In this paper, some results about approximation in a norm S induced by the minimax series are studied. Then a Bernstein-type theorem for the norm S is established. Finally the Bernstein theorem is applied to prove the existence of certain equalities with minimax series and weighted minimax series.展开更多
文摘We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.
基金supported by National Natural Science Foundation of China (Grant Nos. 11101129, 11201318 and 11171091)supported by National Natural Science Foundation of China (Grant No. 11126328)+2 种基金Natural Science Foundation of He'nan Provincial Education Committee (Grant No. 12B110014)Project for Young Key Teachers of He'nan Normal Universitythe general scientific research project of the Education Department of Guangxi Province (Grant No. 201102ZD007)
文摘Let f be a smooth strictly convex solution ofdefined on a domain Ω C R^n, where ai, bi and c are constants. Then the graph Mvf of △f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space with the translating vector（al, a2, . ., an; bz, b2, , bn）. In this paper, we will use alCfine technique to show a Berustein Theorem： if the graph Mvf is complete, then f（x） must be a quadratic polynomial and Mvf is an ailine n-plane.
文摘In this paper, some results about approximation in a norm S induced by the minimax series are studied. Then a Bernstein-type theorem for the norm S is established. Finally the Bernstein theorem is applied to prove the existence of certain equalities with minimax series and weighted minimax series.
