论文标题
欧几里得等同步的光谱决定因素，固定区域的三角形信封是角度的函数：绝对最小值和小角度渐近线
Spectral determinant on Euclidean isosceles triangle envelopes of fixed area as a function of angles: absolute minimum and small-angle asymptotics
论文作者
论文摘要
我们研究了弗里德里希（Friederichs）决定因素的极端特性，在欧几里德等同步等质等于固定区域的三角形信封上是固定区域的函数。小角度的渐近学表明，作为三角形的角度，决定因素在没有任何结合的情况下生长为零。我们证明，等边三角形包络（最对称的几何形状）始终导致决定因素的临界点并找到临界值。此外，如果信封的面积不大，则决定因素仅在等边三角形包膜上实现其绝对最小值，并且没有其他临界点，而对于足够大的面积，等边三角形包封对应于确定性的局部最大值。
We study extremal properties of the determinant of Friederichs selfadjoint Laplacian on the Euclidean isosceles triangle envelopes of fixed area as a function of angles. Small-angle asymptotics show that the determinant grows without any bound as an angle of triangle envelope goes to zero. We prove that the equilateral triangle envelope (the most symmetrical geometry) always gives rise to a critical point of the determinant and find the critical value. Moreover, if the area of envelopes is not too large, then the determinant achieves its absolute minimum only on the equilateral triangle envelope and there are no other critical points, whereas for sufficiently large area the equilateral triangle envelope corresponds to a local maximum of the determinant.
