https://neckpinch.com/authors/peng-wu/New arXiv papers by Peng Wu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1911.02729/arxiv:1911.02729Thu, 07 Nov 2019 00:00:00 GMTJia-Yong Wu, Peng Wu — In this paper, we study harmonic and caloric functions of polynomial growth on a complete non-compact gradient shrinking Ricci soliton. On one hand, when the scalar curvature satisfies at least quadratic decay, we prove that the space of harmonic functions with fixed polynomial growth degree is finite dimensional. We also prove analogous results for ancient caloric functions. On the other hand, without any curvature condition, we prove sharp finite dimensional estimates for the space of Schrödinger functions with fixed polynomial growth degree.Ricci solitonsAncient solutionsScalar curvatureBoundaries & non-compact https://neckpinch.com/papers/1903.11817/arxiv:1903.11817Thu, 28 Mar 2019 00:00:00 GMTPeng Wu — For Einstein four-manifolds with positive scalar curvature, we derive relations among various positivity conditions on the curvature tensor, some of which are of great importance in the study of the Ricci flow. These relations suggest possible new ideas to study the well-known rigidity conjecture for positively curved Einstein four-manifolds.Ricci flow4-manifoldsScalar curvatureStability & uniqueness