Xuwen Zhang (张旭文)
About Me.
I am a PhD student at Xiamen University, supervised by Chao Xia, I am expected to graduate this May. From 03/2023 to 03/2024, I was a Visiting Ph.D. student at Goethe-Universität Frankfurt am Main, hosted and co-supervised by Julian Scheuer.
My research focuses on Geometric Analysis, especially in capillary surfaces, anisotropic geometry, and geometry of varifolds.
My full CV is here.
Email: math[dot]xuwenzhang[at]gmail[dot]com
Preprints
Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space, with Xiaohan Jia, preparing for submission. [arXiv: 2403.06597]
Stability of the Wulff shape with respect to anisotropic curvature functionals, with Julian Scheuer, submitted. [arXiv: 2308.15999]
Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces, with Xiaohan Jia, Zheng Lu, and Chao Xia, submitted. [arXiv: 2311.18585]
A characterization of capillary spherical caps by a partially overdetermined problem in a half ball, with Xiaohan Jia, Zheng Lu, and Chao Xia, submitted. [arXiv: 2311.18581]
Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space, with Chao Xia, submitted. [arXiv: 2304.01735]
Heintze-Karcher inequality and capillary hypersurfaces in a wedge, with Xiaohan Jia, Guofang Wang, and Chao Xia, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. [arXiv: 2209.13839]
Publications
A boundary maximum principle for stationary pair of varifolds with fixed contact angle, Proc. Edinb. Math. Soc. [FirstView]
Capillary Schwarz symmetrization in the half-space, with Zheng Lu and Chao Xia, Adv. Nonlinear Stud. 23 (2023), no. 1, Paper No. 20220078.
Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space, with Xiaohan Jia, Guofang Wang, and Chao Xia, Arch. Ration. Mech. Anal. 247 (2023), no.2, Paper No. 25.
A Heintze-Karcher type inequality for hypersurfaces with capillary boundary, with Xiaohan Jia and Chao Xia, J. Geom. Anal. 33 (2023), no.6, Paper No. 177. [Published Version]
C^{1,1}-rectifiability and Heintze-Karcher inequality on S^{n+1}, ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 47.
Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball, with Chao Xia, Adv. Calc. Var. [Ahead of Print]
Miscellaneous
Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains, with Xiaohan Jia, Guofang Wang, and Chao Xia, submitted.
Research talks
Advanced Seminar Geometric Analysis, University of Freiburg, 12/2023. [slides]
Oberseminar Geometrische Analysis, Goethe-Universität Frankfurt, 04/2023. [slides]
The 4th Geometric Analysis Festival, 11/2021.
Dissertations
Doctoral Thesis: Alexandrov’s Theorem for Capillary Hypersurfaces. (in Chinese [English version]), Xiamen University, April, 2024.
Bachelor Thesis: Proof of Aleksandrov's Theorem, (in Chinese), Xiamen University, June, 2019.