https://neckpinch.com/authors/guangwen-zhao/New arXiv papers by Guangwen Zhao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2607.28057/arxiv:2607.28057Thu, 30 Jul 2026 00:00:00 GMTGuangwen Zhao — We study Liouville-type theorems for real-valued pluriharmonic functions on complete gradient Kähler-Ricci solitons under gradient integrability assumptions. For a complete gradient Kähler-Ricci soliton (M,g,J,f) and a real-valued pluriharmonic function u, we investigate conditions under which u must be constant. By introducing a globally defined holomorphic quantity induced by the soliton potential, we obtain new Liouville-type results beyond the range available for harmonic functions. In the steady case, we prove that u is constant whenever ∫_M|∇u|^pdv<∞ for some 0<p<∞. In the shrinking case, we prove the same conclusion for 0<p≤ 2. Finally, we construct a complete Kähler example showing that the extension to the range 0<p<1 relies essentially on the soliton structure and does not hold on general complete Kähler manifolds.Ricci solitonsKähler–Ricci solitonsKähler geometry