Poster References
The following are references for the poster Heat Kernel and Spectral Estimates Under Integral Curvature Bounds, which was presented at the conference Heat Kernels and Stochastic Analysis, celebrated from June 29th to July 3rd at Aarhus University.
References for spectral estimates under integral curvature
The main eigenvalue estimate presented in the poster can be found in reference [1] below, although the work there is an improvement of previous work [2]. In [3] we show that smallness of the integral curvature is a necessary condition. Finally, [4] showcases other spectral estimates under integral curvature conditions.
References for heat kernel estimates under integral curvature
The main heat kernel estimate presented in the poster can be found in reference [1] below, although that estimate requires the work in [2] to be fully correct as stated in the poster. In [3] we show a gradient estimate for a non-linear parabolic equation, which is proven in the same spirit as [1].
References for spectral estimates under integral curvature
The main eigenvalue estimate presented in the poster can be found in reference [1] below, although the work there is an improvement of previous work [2]. In [3] we show that smallness of the integral curvature is a necessary condition. Finally, [4] showcases other spectral estimates under integral curvature conditions.
- Sharp Spectral Gap Estimates on Manifolds under Integral Ricci Curvature Bounds, joint with Shoo Seto and Malik Tuerkoen. Preprint, submitted for publication (2025).
- Zhong-Yang type eigenvalue estimate with integral curvature condition, joint with Shoo Seto, Guofang Wei, and Qi S. Zhang. Mathematische Zeitschrift 296, 595-613 (2020). https://doi.org/10.1007/s00209-019-02448-w.
- Manifolds with bounded integral curvature and no positive eigenvalue lower bounds, joint with Connor C. Anderson and Kamryn Spinelli. The PUMP Journal of Undergraduate Research, 4, 222–235 (2021).
- Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains, joint with Christian Rose, Lili Wang, and Guofang Wei. Mathematische Nachrichten 296, 8 (2023), 3559–3578. https://doi.org/10.1002/mana.202100523
References for heat kernel estimates under integral curvature
The main heat kernel estimate presented in the poster can be found in reference [1] below, although that estimate requires the work in [2] to be fully correct as stated in the poster. In [3] we show a gradient estimate for a non-linear parabolic equation, which is proven in the same spirit as [1].
- Neumann Li-Yau gradient estimate under integral Ricci curvature bounds, Proceedings of the American Mathematical Society, 147, No. 1, January 2019, Pages 411–426.
- Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions, joint with Olaf Post and Christian Rose. Journal of Geometric Analysis 33, 70 (2023). https://doi.org/10.1007/s12220-022-01118-4.
- Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition, joint with Shoo Seto. Differential Geometry and its Applications 98, 102222 (February 2025), https://doi.org/10.1016/j.difgeo.2024.102222.
