講題：Rigidity and Classification of Graphical Mean Curvature Flow Translators and λ-Translators
講者：黃垣熊博士後(國家理論科學研究中心)
時間：115年3月23日下午12：20-13：10
地點：民生校區五育樓401教室
摘要
Translating solitons play a central role as singularity models in Mean Curvature Flow (MCF). In this talk, we present new rigidity and classification results for two classes of these hypersurfaces: graphical MCF translators moving in arbitrary directions and generalized λ-translators.
First, we show that entire graphical surfaces translating in non-vertical directions must be the flat plane if they are mean convex or have small entropy. We extend these results to higher dimensions under specific growth conditions on the height function.
Second, we examine λ-translators, which generalize the MCF translator via the weighted mean curvature equation. After introducing a notion of stability for these hypersurfaces, we prove that stable λ-translators with finite weighted curvature are hyperplanes under certain integral or pointwise curvature conditions. We conclude with classification results for entire graphical λ-translators with bounded gradients.