On the rigidity theorems for lagrangian translating solitons in pseudo-Euclidean space I

Rigidity of complete spacelike translating solitons in pseudo-Euclidean space

“…Firstly, we classify m-dimensional complete spacelike translating solitons in R m+n n by affine technique and classical gradient estimates, and prove the only complete spacelike translating solitons in R m+n n are the spacelike m-planes. This result provides another proof of a nonexistence theorem for complete spacelike translating solitons in [8], and a simple proof of rigidity theorem in [33]. Secondly, we generalize the rigidity theorem of entire spacelike Lagrangian translating solitons in [34] to spacelike translating solitons with general codimensions.…”

“…Here we only investigate the rigidity of spacelike translating soliton in R m+n n . For complete spacelike Lagrangian translating solitons in R 2n n , Xu-Huang [33] proved the following rigidity theorem.…”

“…In fact, such nonexistence conclusion still holds for the lightlike translating vector case. Motivating by papers [8,33], we classify m-dimensional complete spacelike translating solitons in R m+n n by affine technique and classical gradient estimates, and obtain the following Bernsterin theorem.…”

On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space III

“…In [18], the first author and Huang proved the following estimate for the function defined above. f (x 1 , .…”

“…, b n ), for details see [18]. In [18], the first author and Huang proved a Bernstein theorem for complete translating solitons as follows:…”