论文标题
简单气泡树附近的a lojasiewicz不平等现象
Łojasiewicz inequalities near simple bubble trees
论文作者
论文摘要
在本文中，当$ h $是恒定时，我们证明了$ h $功能的关键点的差距现象，而在这种情况下，在这种设置中，几乎关键点的序列还满足了第一批非平凡的泡泡树时，几乎关键点的序列满足了olojasiewicz的不平等现象。 为了证明这些结果，我们得出了足够的条件，使lojasiewicz的不平等现象在希尔伯特空间上的合适功能几乎临界点附近保持有限维度的次要数。
In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree. To prove these results we derive sufficient conditions for Łojasiewicz inequalities to hold near a finite-dimensional submanifold of almost-critical points for suitable functionals on a Hilbert space.
