The isoperimetric ratio of an embedded surface in $R^3$ is defined as theratio of the area of the surface to power three to the squared enclosed volume.The aim of the present work is to study the minimization of the Willmore energyunder fixed isoperimetric ratio when the underlying abstract surface has fixedgenus $g\geq 0$. The corresponding problem in the case of spherical surfaces,i.e. $g=0$, was recently solved by Schygulla with different methods.
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机译：$ R ^ 3 $中的嵌入表面的等压比定义为表面功率乘以3的面积与平方封闭体积的比值。本研究的目的是研究固定等压比下Willmore能量的最小化当底层抽象表面具有固定类$ g \ geq 0 $时。在球形表面的情况下相应的问题$ g = 0 $，最近由Schygulla用不同的方法求解。
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