殷浩
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我从事几何分析领域的研究，主要使用分析工具（尤其是偏微分方程方法）来研究几何问题。我的研究关注临界变分问题的正则性、紧性和存在性，例如二维调和映射与四维Yang-Mills方程。
Ricci 流
研究带/不带锥奇点的曲面上的 Ricci 流，关注解的存在性、唯一性以及渐近行为。
带锥奇点的 Ricci 流
粗糙初值的 Ricci 流
调和映射
研究调和映射与双调和映射的存在性、正则性和爆破行为，发展退化序列的颈部分析方法。
双调和映射的正则性
颈部分析
切锥唯一性
爆破现象
Yang-Mills 理论
探索 Yang-Mills 方程及其几何应用，研究四维情形下的爆破行为以及 α-流逼近。
Yang-Mills 流
四维爆破
α-流逼近
极小化方法
Willmore 曲面
研究 Willmore 曲面的紧性及其几何性质，发展三圆定理并分析复结构的退化。
三圆定理
复结构退化
变分问题
研究兴趣
我的研究位于偏微分方程与微分几何的交叉领域，尤其关注几何流（如 Ricci 流）在奇异空间上的行为，以及调和映射和 Yang-Mills 场的正则性/紧性理论。通过对非线性偏微分方程的细致分析，我希望揭示几何变分问题的基本性质。
论文与预印本
预印本
Y. Li and H. Yin, On the Ends of Willmore Surfaces with Curvature Decay, arXiv preprint, 2026.
A. Waldron and H. Yin, The Yang-Mills equation near instanton-anti-instanton configurations, arXiv preprint, 2026.
H. Qian and H. Yin, On the blow-up of harmonic maps from surfaces to homogeneous manifolds, arXiv preprint, 2026.
Y. Li, H. Yin, and J. Zhou, 3-circle Theorem for Willmore surface II -- degeneration of the complex structure, arXiv preprint, 2024.
H. Yin, On the blow-up of Yang-Mills fields in dimension four, arXiv preprint, 2023.
已发表论文
B. Wang and H. Yin, Curvature at the infinity of asymptotically flat Einstein manifold, To appear in Trans. Amer. Math. Soc., 2025.
Y. Li and H. Yin, 3-circle Theorem for Willmore surface I, J. London Math. Soc., 2025.
P.M. Topping and H. Yin, Smoothing a measure on a Riemann surface using Ricci flow, Ars Inveniendi Analytica, 2024.
P.M. Topping and H. Yin, Uniqueness of Ricci flows from nonatomic Radon measures on Riemann surfaces, Proc. London Math. Soc. 128, e12600, 2024.
H. Yin, Direct minimizing method for Yang-Mills energy over SO(3) bundle, Math. Ann., 2023.
H. Yin, Analysis aspects of Ricci flow on conical surfaces, Acta Math. Sinica (Engl. Ser.) 38, 807-857, 2022.
H. Yin, Higher order neck analysis of harmonic maps and its applications, Ann. Global Anal. Geom. 62, 401-438, 2022.
Y. Gui and H. Yin, Schauder estimates on smooth and singular spaces, Ann. Global Anal. Geom. 59, 457-481, 2021.
H. Yin, Generalized neck analysis of harmonic maps from surfaces, Calc. Var. Partial Differential Equations 60, Paper No. 117, 2021.
P.M. Topping and H. Yin, Rate of curvature decay for the contracting cusp Ricci flow, Comm. Anal. Geom. 28, 1221-1250, 2020.
Y. Chen and H. Yin, Uniqueness of tangent cone for biharmonic map with isolated singularity, Pacific J. Math. 299, 401-426, 2019.
K. Zheng and H. Yin, Expansion formula for complex Monge-Ampère equation along cone singularities, Calc. Var. PDE 59, art.no.50, 2019.
P.M. Topping and H. Yin, Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces, Ann. PDE 3, Art. 6, 2017.
W. Ai and H. Yin, Neck analysis of extrinsic polyharmonic maps, Ann. Global Anal. Geom. 52, 129-156, 2017.
L. Liu and H. Yin, Neck analysis for biharmonic maps, Math. Z. 283, 807-834, 2016.
L. Liu and H. Yin, On the finite time blow-up of biharmonic map flow in dimension four, J. Elliptic Parabol. Equ. 1, 363-385, 2015.
M.C. Hong, G. Tian, and H. Yin, The Yang-Mills α-flow in vector bundles over four manifolds and its applications, Comment. Math. Helv. 90, 75-120, 2015.
M.C. Hong and H. Yin, On the Sacks-Uhlenbeck flow of Riemannian surfaces, Comm. Anal. Geom. 21, 917-955, 2013.
M.C. Hong and H. Yin, Partial regularity of the relaxed energy for biharmonic maps, J. Funct. Anal. 262, 681-718, 2012.
M. Giaquinta, M.C. Hong, and H. Yin, A new approximation of relaxed energies for harmonic maps and Faddeev model, Calc. Var. PDE 41, 45-69, 2011.
H. Li and H. Yin, On stability of hyperbolic space form under the normalized Ricci flow, Int. Math. Res. Not. 2010, 2903-2924, 2010.
H. Yin, Ricci flow on surfaces with conical singularities, J. Geom. Anal. 20, 970-995, 2010.
H. Yin, Normalized Ricci flow on nonparabolic surfaces, Ann. Global Anal. Geom. 36, 81-104, 2009.
H. Yin, Boundary regularity of harmonic maps from hyperbolic space into nonpositively curved manifolds, Pacific J. Math. 232, 491-509, 2007.
W. Ding and H. Yin, Special periodic solutions of Schrödinger flow, Math. Z. 253, 555-570, 2006.
H. Yin, Periodic solutions of Schrödinger flow from S³ to S², Chinese Ann. Math. Ser. B 27, 401-410, 2005.
（更多论文信息请参见 个人主页 或相关学术数据库。）
