A list of my papers

1. Whitney-Graustein 微分同伦的曲率流实现问题（Yau 问题) 
[1-3] Gao, Laiyuan; Wang, Zheqi Evolving an immersed star-shaped curve to another one with same winding number. Submitted.
[1-2] Gao, Laiyuan Whitney-Graustein homotopy of locally convex curves via a curvature flow. Math. Res. Lett. 30 (2023), no. 4, 1045–1062.
[1-1] Gao, Laiyuan; Zhang, Yuntao On Yau's problem of evolving one curve to another: convex case. J. Differential Equations  266  (2019),  no. 1, 179–201. 

2. 等宽曲线、等宽超曲面与曲率流
[2-3] Gao, Laiyuan; Martini, Horst; Zhang, Deyan Deforming locally convex curves into curves of constant k-order width. Differential Geom. Appl. 97 (2024), Paper No. 102192, 15 pages.
[2-2] Gao, Laiyuan; Zhang, Yuntao Evolving convex surfaces to constant width ones. Internat. J. Math.  28  (2017),  no. 11, 1750082, 18 pp. 
[2-1] Gao, Laiyuan; Pan, Shengliang Evolving convex curves to constant-width ones by a perimeter-preserving flow. Pacific J. Math.  272  (2014),  no. 1, 131–145.

3. 非局部曲率流问题
[3-7] Gao, Laiyuan; Pan, Shengliang Evolving convex curves by a generalized length-preserving flow. arXiv:2012.11549.
[3-6] 高来源，郝瑞霞，潘生亮 非局部平面曲线流——献给姜礼尚教授90华诞. 中国科学-数学，No.3, 54 (2024), 407 - 422.  
[3-5] Gao, Laiyuan; Pan, Shengliang Star-shaped centrosymmetric curves under Gage's area-preserving flow. J. Geom. Anal. 33 (2023), no. 11, Article No. 348, 25 pages.
[3-4] Gao, Laiyuan; Pan, Shengliang; Shi, Ke A log-type non-local flow of convex curves. Comm. Anal. Geom.  29  (2021),  no. 5, 1157–1182. 
[3-3] Gao, Laiyuan; Pan, Shengliang; Tsai, Dong-Ho On an area-preserving inverse curvature flow of convex closed plane curves. J. Funct. Anal.  280  (2021),  no. 8, Paper No. 108931, 31 pages.
[3-2] Gao, Laiyuan; Pan, Shengliang; Tsai, Dong-Ho Nonlocal flow driven by the radius of curvature with fixed curvature integral. J. Geom. Anal.  30  (2020),  no. 3, 2939–2973. 
[3-1] Gao, Laiyuan; Pan, Shengliang; Tsai, Dong-Ho On a length-preserving inverse curvature flow of convex closed plane curves. J. Differential Equations  269  (2020),  no. 7, 5802–5831. 

4. 几何不等式
[4-3] Gao, Laiyuan; Zhang, Zhongyun; Zhou, Fei An extension of Rabinowitz's polynomial representation for convex curves. Beitr. Algebra Geom.  61  (2020),  no. 3, 455–464. 
[4-2] Gao, Laiyuan; Pan, Shengliang; Yang, Yunlong Some notes on Green-Osher's inequality. J. Math. Inequal.  9  (2015),  no. 2, 369–380.
[4-1] Gao, Laiyuan; Wang, Yiling Deforming convex curves with fixed elastic energy. J. Math. Anal. Appl.  427  (2015),  no. 2, 817–829.

5. 曲线收缩流、高维外蕴曲率流
[5-3] Gao, Laiyuan; Zhang, Yuntao; Zhang, Shicheng Star-shaped Curves under Gage's Area-preserving Flow and the CSF. arXiv:2412.18102
[5-2] Gao, Laiyuan; Zhang, Yuntao Evolving compact locally convex curves and convex hypersurfaces. Manuscripta Math.  167  (2022),  no. 1-2, 365–375. 
[5-1] Gao, Laiyuan; Pan, Shengliang Gage's original normalized CSF can also yield the Grayson theorem. Asian J. Math.  20  (2016),  no. 4, 785–794. 

6. Ricci 流、其他内蕴曲率流
[6-1] in preparation

7. 流形的特征值问题
[7.1] in preparation

8. 高阶曲率流
[8-1] Gao, Laiyuan; Tsai, Dong-Ho On a third order flow of convex closed plane curves. Taiwanese J. Math.  20  (2016),  no. 3, 553–567. 



我在 arxiv.org
https://arxiv.org/search/?searchtype=author&query=Gao%2C+Laiyuan