发表机构
Mathematics and Science College, Shanghai Normal University（上海师范大学数理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究单位圆柱内径向图在幂平均曲率流（$V=H^\alpha+b$）下的演化，证明高度、梯度界及紧性，识别平移极限为杯形平移子，并涵盖静止帽与幂律Robin边界条件。
AI 中文摘要
我们研究在单位圆柱内，由$V=H^\alpha+b$（其中$\alpha>0$，$b<0$）驱动且满足$u_r(1,t)=u(1,t)$的正径向图。我们将有限时间延拓估计与归一化平移收敛所需的时间一致内部估计分开处理。在已有的经典区间上，我们证明了高度和梯度界，以及将速度界显式转换为$H$、$u_r/r$和$u_{rr}$的估计。我们推导了与有限斜率平移子比较时正确的边界缺陷。在独立的内部速度界和两侧斜率受限条件下，我们证明了紧性，并将每个平移极限识别为杯形平移子。我们指出了建立该受限条件仍需要的径向零点比较。还包括静止帽和幂律Robin定律的情形。
英文摘要
We study a positive radial graph evolving by $V=H^α+b$, with $α>0$ and $b<0$, in the unit cylinder and with $u_r(1,t)=u(1,t)$. We separate finite-time continuation estimates from the time-uniform interior estimates needed for convergence of normalized translates. On existing classical intervals we prove height and gradient bounds and an explicit conversion of velocity bounds into estimates for $H$, $u_r/r$, and $u_{rr}$. We derive the correct boundary defect for comparisons with finite-slope translators. Under independent interior velocity bounds and two-sided slope trapping, we prove compactness and identify every translated limit with the cup translator. We identify the radial zero-number comparison still required to establish that trapping. Stationary caps and power-law Robin laws are included.
