科研项目(Research Grants) 国家自然科学基金青年基金，1210010723，对两类绝热问题中若干数学问题的研究，2022/01-2024/12，30万，在研，主持。 研究兴趣和主要论文(Research Interest with Representative Papers) (1) Semilinear Elliptic Equations and Conformal Geometry [1] Gui, Changfeng; Li, Qinfeng; Completion of R^2 with a Conformal Metric as a Closed Surface, Anal. Theory Appl., 37, 59-73, 2021. DOI: 10.4208/ata.2021.pr80.10. (Dedicated to Paul H. Rabinowitz for his 80’s birthday) [2] Gui, Changfeng; Li, Qinfeng; Some energy estimates for stable solutions to fractional Allen-Cahn equations, Calculus of Variations and Partial Differential Equations, 59(2): 1-17, 2020. [3] Gu, Guangze; Gui, Changfeng; Hu, Yeyao; Li, Qinfeng; Uniqueness and Symmetry for the Mean Field Equation on Arbitrary Flat Tori, International Mathematics Research Notices, 2020. DOI: 10.1093/imrn/rnaa109. [4] Gui, Changfeng; Li, Qinfeng. Some geometric inequalities on Liouville equation. Preprint, 2021. [5] Li, Qinfeng; Xu, Lu. A stronger constant rank theorem. Preprint, 2021. (2) Geometric Measure Theory and its Applications in Geometric Variational Problems [1] Gui, Changfeng; Hu, Yeyao; Li, Qinfeng; On smooth interior approximation of sets of finite perimeter, Proceedings of American Mathematical Society (accepted), 2021. https://www.ams.org/cgi-bin/mstrack/accepted_papers/proc. [2] Du, Hengrong; Li, Qinfeng; Wang, Changyou; Compactness of M-uniform domains and optimal thermal insulation problems, Advances in Calculus of Variations, 2021. https://doi.org/10.1515/acv-2020-0088. [3] Chen, Gui-Qiang; Li, Qinfeng; Torres, Monica; Traces and extensions of bounded divergence-measure fields on rough open sets, Indiana University Mathematics Journal, 69(1): 229-264, 2020. [4] Li, Qinfeng; Torres, Monica; Morrey spaces and generalized Cheeger sets, Advances in Calculus of Variations, 12(2): 111-133, 2019. [5]Bright, Ido; Li, Qinfeng; Torres, Monica*; Occupational measures and averaged shape optimization, ESAIM: Control, Optimization and Calculus of Variations, 24(3): 1141-1165, 2018. [6] Li, Qinfeng; Wang, Changyou. On Nematic liquid crystal droplets. Preprint. [7] Gui, Changfeng; Hu, Yeyao; Li, Qinfeng. Extensions and Traces of BV functions on Rough domains and Generalized Cheeger sets. Preprint, 2021. (3) Ellipticc Eigenvalue Problems with Applications [1] Huang, Yong; Li, Qinfeng; Li, Qiuqi. Two thermal insulation problems and a new eigenvalue problem. arXiv: 2011.00291. 2021. [2] Huang, Yong; Li, Qinfeng; Li, Qiuqi; Yao, Ruofei. On Laplacian eigenvalue problem with -1 Neumann boundary condition. Preprint, 2021. 教授课程（Teaching）2021 Fall: Probability and Statistics A (For undergraduate students)， Hunan University 2021 Spring: Spectral Theory and Shape Optimization Problems (Research Seminar), Hunan University 2020 Fall: Probability and Statistics A (For undergraduate students), Hunan University. Spring 2020: Calculus 2 Instructor, UTSA. Fall 2019: Calculus 3 Instructor, UTSA. Spring 2019: Calculus 3 Instructor, UTSA Spring 2017: Calculus 3 Recitation Instructor, Purdue University. Fall 2016: Calculus 3 Recitation Instructor, Purdue University. Spring 2016: Calculus 3 Recitation Instructor, Purdue University. Fall 2015: Calculus 1 Recitation Instructor, Purdue University.
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