Hilbert volume is an invariant of real projective geometry. Polygons inscribed in polygons are considered for the real projective plane. In two-dimensions the correspondence between Fock–Goncharov and Cartesian coordinates is examined. Degeneration and Hilbert area of inscribed quadrilaterals are analyzed. A microlocal condition is developed for bounded Hilbert area under degeneration. The condition is applied to give a sequence of strictly convex domains with bounded Hilbert area and divergent Goldman parameters.

中文翻译：

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内接三角形和四边形的希尔伯特区域

希尔伯特体积是实际射影几何的不变式。多边形中刻出的多边形被认为是真实的投影平面。在二维中，检查了Fock–Goncharov和笛卡尔坐标之间的对应关系。分析了内接四边形的退化和希尔伯特面积。针对退化下的有限希尔伯特区域，建立了一个微局部条件。该条件适用于给出一系列有界希尔伯特面积和发散高盛参数的严格凸域。