Schroedinger算子的Lieb-Thirring猜想与平面上椭圆的等周问题之间的联系
Connection between the Lieb--Thirring conjecture for Schroedinger operators and an isoperimetric problem for ovals on the plane
摘要：
确定（1/2，3/2）中具有指数γ的一维Lieb-Thirring不等式的锐常数是一个公开问题.根据Lieb和Thirring的猜想，这些指数的尖锐常数应该通过只有一个束缚态的势来获得。在这里，我们展示了一个连接之间的Lieb-Thirring猜想伽玛=1和isporimetric不等式的椭圆在平面上。
英文摘要：
To determine the sharp constants for the one dimensional Lieb--Thirring inequalities with exponent gamma in (1/2,3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be attained by potentials having only one bound state. Here we exhibit a connection between the Lieb--Thirring conjecture for gamma=1 and an isporimetric inequality for ovals in the plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
