This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature...This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.展开更多
We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance functi...We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps.展开更多
In this paper, we investigate the positive solutions of ■u =■υ/■t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.
目的检索美国食品药品监督管理局(Food and Drug Administration,FDA)不良事件报告系统(Adverse Event Reporting System,FAERS)数据库,分析罗莫单抗(Romosozumab)相关药物不良事件(Adverse Drug Event,ADE),为临床用药提供参考。方法...目的检索美国食品药品监督管理局(Food and Drug Administration,FDA)不良事件报告系统(Adverse Event Reporting System,FAERS)数据库,分析罗莫单抗(Romosozumab)相关药物不良事件(Adverse Drug Event,ADE),为临床用药提供参考。方法回顾性查询2019年4月1日至2024年1月31日的美国FAERS数据库,提取Romosozumab相关报告。采用报告比值比(Reporting Odds Ratio,ROR)、比例报告比(Proportional Reporting Ratio,PRR)、贝叶斯可信区间递进神经网络(Bayesian Confidence Propagation Neural Network,BCPNN)和多项式伽马泊松分布缩减(Multi-Item Gamma Poisson Shrinker,MGPS)等方法识别和评估Romosozumab相关ADE。结果共检索到8432351例ADE报告,其中7477例Romosozumab“主要疑似”报告。Romosozumab在16个系统-器官(System Organ Class,SOC)中关联195个ADE信号,主要涉及损伤/中毒、全身性疾病、肌肉骨骼疾病和心脏疾病。常见的ADE包括骨折、骨密度异常、注射部位反应、关节痛、肢体疼痛和心脏事件。此外,一些未在说明书中记载的ADE,如椎体压缩骨折、桡骨骨折、血甲状旁腺素升高和肾功能损害,也显示出较高的信号值。Romosozumab的严重事件包括住院和死亡。结论本研究确认Romosozumab相关的常见ADE,临床需注意未在药品说明书中记载的ADE,如新的骨折或骨密度异常,并采取相应预防措施。展开更多
This is the second paper in the series to study the generic dynamics of mean curvature flows.We study the initial perturbation of mean curvature flows,whose first singularity is modeled by an asymptotically conical sh...This is the second paper in the series to study the generic dynamics of mean curvature flows.We study the initial perturbation of mean curvature flows,whose first singularity is modeled by an asymptotically conical shrinker.The noncompactness of the limiting shrinker creates essential difficulties.We introduce the Feynman-Kac formula to get precise asymptotic behaviour of the linearized rescaled mean curvature equation along an orbit.We also develop the invariant cone method for the noncompact setting for the local dynamics near the shrinker.As a consequence,we prove that after a generic initial perturbation,the perturbed rescaled mean curvature flow avoids the conical singularity.展开更多
基金supported by the YSBR-001,the NSFC(12201597)research funds from USTC(University of Science and Technology of China)and CAS(Chinese Academy of Sciences)+2 种基金supported by the YSBR-001the NSFC(11971452,12026251)a research fund from USTC.
文摘This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
基金Supported by National Natural Science Foundation of China(Grant No.11271072)He’nan University Seed Fund
文摘We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps.
基金Project supported by the National Natural Science Foundation of China(Grant No.11271343)the Natural Science Foundation of the Higher Education Institutions of Anhui(Grant No.KJ2018A0059)
文摘In this paper, we investigate the positive solutions of ■u =■υ/■t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.
基金supported by National Natural Science Foundation of China (Grant No.12271285)the New Cornerstone Investigator Programthe Xiaomi Foundation
文摘This is the second paper in the series to study the generic dynamics of mean curvature flows.We study the initial perturbation of mean curvature flows,whose first singularity is modeled by an asymptotically conical shrinker.The noncompactness of the limiting shrinker creates essential difficulties.We introduce the Feynman-Kac formula to get precise asymptotic behaviour of the linearized rescaled mean curvature equation along an orbit.We also develop the invariant cone method for the noncompact setting for the local dynamics near the shrinker.As a consequence,we prove that after a generic initial perturbation,the perturbed rescaled mean curvature flow avoids the conical singularity.
