55 citations · 69 across the 17 of their papers we have counts for
7 papers · 1 filter
Prescribed Scalar Curvature Problem under Conformal Deformation of A Riemannian Metric with Dirichlet Boundary Condition
Jie Xu
In this article, we first show that for all compact Riemannian manifolds with non-empty smooth boundary and dimension at least 3, there exists a metric, pointwise conformal to the…
Prescribed Scalar Curvature on Compact Manifolds Under Conformal Deformation
Jie Xu
We give sufficient and "almost" necessary conditions for the prescribed scalar curvature problems within the conformal class of a Riemannian metric for both closed manifolds…
The Boundary Yamabe Problem, II: General Constant Mean Curvature Case
Jie Xu
This article uses the iterative schemes and perturbation methods to completely solve the Han-Li conjecture, i.e. the general boundary Yamabe problem with prescribed constant scalar…
The Boundary Yamabe Problem, I: Minimal Boundary Case
Jie Xu
We apply iteration schemes and perturbation methods to provide a complete solution of the boundary Yamabe problem with minimal boundary scenario, or equivalently, the existence of…
Solving the Yamabe-Type Equations on Closed Manifolds by Iteration Schemes
Jie Xu
We introduce a double iterative scheme and local variational method to solve the Yamabe-type equation …
Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain
Steven Rosenberg, Jie Xu
We introduce an iterative scheme to solve the Yamabe equation on small domains equipped with a Riemannian metric . T…
Wave Approximation of Backward Heat Equation with Ricci Flow
Jie Xu
In this paper, we consider solutions of the backward heat equation with Ricci flow on manifolds as a type of infinite dimensional limit of solutions of a wave equation on a larger…