On the Rigidity Theorems for Lagrangian Translating Solitons in Pseudo-Euclidean Space Ⅰ  

作　　者：Rui Wei XU Rong Li HUANG 

机构地区：[1]Department of Mathematics, He'nan Normal University [2]Department of Mathematics, Guangxi Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第7期1369-1380,共12页数学学报（英文版）

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);Natural Science Foundation of He'nan Provincial Education Committee (Grant No. 12B110014);Project for Young Key Teachers of He'nan Normal University;the general scientific research project of the Education Department of Guangxi Province (Grant No. 201102ZD007)

摘　　要：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.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.

关 键 词：Mean curvature flow translating solitons Monge-Amp^re equation Bernstein Theorem 

分 类 号：O184[理学—数学]