Research profile

Peng Wu

Works on scalar curvature, 4-manifolds and ancient solutions.

NP-RC-613222

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Scalar curvature4-manifoldsAncient solutionsBoundaries & non-compactStability & uniquenessRicci solitonsRicci flow

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  1. Jia-Yong Wu

    1 joint worklatest 2019

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2019

math.DGv6arXiv:1911.02729

Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons

Jia-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
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math.DGarXiv:1903.11817

Curvature decompositions on Einstein four-manifolds

Peng 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
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A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.