Square-integrability of solutions of the Yamabe equation

梯度h-几乎Yamabe孤子的平凡性与数量曲率估计

On triviality and scalar curvature estimation of gradient h-almost Yamabe solitons

研究紧致与完备非紧黎曼流形上的梯度h-几乎Yamabe孤子，通过积分不等式给出平凡性条件，并在L^2可积条件下获得数量曲率估计，推广了先前结果。

Integrability theorems and conformally constant Chern scalar curvature metrics in almost Hermitian geometry

The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the Kähler case. Our main question is the existence of almost Kähler metrics with conformally constant Chern scalar curvature. This problem is completely solved for ruled manifolds and in a complementary case where methods from the Chern-Yamabe problem are adapted to the non-integrable case. Also a moment map interpretation of the problem is given, leading to a Futaki invariant and …

边界 Yamabe 问题中紧致性的临界维数，II

On Critical Dimensions for Compactness in the Boundary Yamabe Problem, II

本文确定了边界 Yamabe 问题中紧致性的临界维数，给出不同边界条件下的尖锐范围，并通过标量修正与几何公式证明过渡维数。

紧致 Hermitian 流形上的形变 Gauduchon-Yamabe 问题

Deformed Gauduchon-Yamabe problems on compact Hermitian manifolds

本文研究紧致 Hermitian 流形上 Gauduchon 联络的标量曲率形变，给出常曲率度量存在判据，并分析 Yamabe 不变量的全局依赖性及临界阈值应用。

海森堡群上CR Yamabe方程正整体解的分类

Classification of positive entire solutions of the CR Yamabe equation on the Heisenberg group

该研究完成了海森堡群上临界CR Yamabe方程正整体解的维度分类，通过利用Green表示的推论、共形协变性等，在无能量界的类中隔离出气泡流形，解决了欧氏方法无法适用的问题。

Branson's Q-curvature in Riemannian and Spin Geometry

On a closed 4-dimensional Riemannian manifold, we give a lower bound for the square of the first eigenvalue of the Yamabe operator in terms of the total Branson's Q-curvature. As a consequence, if the manifold is spin, we relate the first eigenvalue of the Dirac operator to the total Branson's Q-curvature. On a closed n-dimensional manifold, $n\ge 5$, we compare the three basic conformally covariant operators : the Branson-Paneitz, the Yamabe and the Dirac operator (if the manifold is spin) through their first eigenvalues. Equality cases are also characterized.