Inverse spectral positivity for surfaces
Inverse spectral positivity for surfaces
复制标题
表面的反光谱正性
DOI：
10.4171/rmi/813
复制
发表时间：
2011
影响因子：
1.2
通讯作者：
P. Castillon
中科院分区：
文献类型：
--
作者：
Pierre B'erard;P. Castillon
设（M，g）是完备的非紧黎曼曲面.我们考虑形式为Δ+aK+W的算子，其中Δ是非负拉普拉斯算子，K是高斯曲率，W是局部可积函数，a是正的真实的数.假设W的正部分是可积的，我们解决了这样一个问题：“从算子Δ+aK+W是非负的这一事实中，我们可以得出关于（M，g）和W的什么结论？“作为主要结果的结果，我们得到了Huber定理和Cohn-Vossen不等式的新证明，并在W为非正的且a=1/4或a∈（0，1/4）的特殊情况下改进了以前的结果.
Let (M,g) be a complete noncompact Riemannian surface. We consider operators of the form Δ+aK+W, where Δ is the nonnegative Laplacian, K the Gaussian curvature, W a locally integrable function, and a a positive real number. Assuming that the positive part of W is integrable, we address the question "What conclusions on (M,g) and on W can one draw from the fact that the operator Δ+aK+W is nonnegative?" As a consequence of our main result, we get new proofs of Huber's theorem and Cohn–Vossen's inequality, and we improve earlier results in the particular cases in which W is nonpositive and a=1/4 or a∈(0,1/4).