Generalised Hörmander-Rellich-Pohozhaev-Morawetz identities and their applications in spectral geometry

谱理论研究的数学模型通常出现在波动，无论是在连续介质力学或量子物理，和抽象的类似物。大多数涉及偏微分方程的问题不能用解析法求解。谱几何研究的基础几何之间的联系和频谱性质的运营商，无论是直接的和inverse.We建议调查一些长的搁浅在谱几何，和一些新的问题，使用乘数的方法通常与Hörmander，Rellich，Pohozhaev和Morawetz的名字。这种方法导致的身份是先验满足的特征函数的边值问题，并可以用来提取相关的几何信息。

Spectral theory studies the mathematical models usually arising in wave motion, either in continuum mechanics or in quantum physics, and the abstract analogues. Most of the problems involving partial differential equations cannot be solved analytically. Spectral geometry studies the links between the underlying geometry and the spectral properties of operators, both direct and inverse.We propose to investigate some long stranding conjectures in spectral geometry, and some new problems, using the method of multipliers commonly associated with the names of Hörmander, Rellich, Pohozhaev and Morawetz. This method leads to identities which are a priori satisfied by eigenfunctions of a boundary value problem, and which can be used to extract the relevant geometric information.