N. Wu

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20092026

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math.DG2026

Prüfer $2$ -group and Milnor's Conjecture on Fundamental Groups

Nan Wu, Zetian Yan

We construct complete, one-ended Riemannian manifolds in dimensions four and five having strictly positive Ricci curvature, with fundamental group isomorphic to the Prüfer $2$ -grou…

math.DG2026

A sharp relative comparison inequality for conformal fillings of Poincaré--Einstein manifolds

Nan Wu

Let $(X^{n + 1}, g_{+})$ be a Poincaré--Einstein manifold with conformal infinity $(M^{n}, [h])$ of positive Yamabe constant $Y (M, [h])$ . Then a relative comparison inequality \[ \frac{Y_1(…

math.DG2025

Energy reduction for Fourth order Willmore energy

Nan Wu, Zetian Yan

We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in $R^{n}$ and establish a connected sum energy reduction for the general…

math.DG2019

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation

Xuezhang Chen, Nan Wu

We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation…

Prüfer 2-group and Milnor's Conjecture on Fundamental Groups

A sharp relative comparison inequality for conformal fillings of Poincaré--Einstein manifolds

Energy reduction for Fourth order Willmore energy

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation

Prüfer $2$ -group and Milnor's Conjecture on Fundamental Groups