超球面中的限制球面
Confining spheres within hyperspheres
摘要：
任何可自由变形的闭曲面的弯曲能都是曲率的平方。在没有约束的情况下，当曲面采用圆球的形式时，它将被最小化。然而，如果表面被限制在一个较小尺寸的超曲面内，这种球形状态就变得不可接近了。引入一个框架来描述受限表面的平衡态。它适用于一个二维表面内的三维超球较小的半径限制。如果多余的表面积很小，平衡态是由两个球的谐波变形：基态是由四极描述，所有更高的多极被证明是不稳定的。
英文摘要：
The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a hypersurface of smaller size, however, this spherical state becomes inaccessible. A framework is introduced to describe the equilibrium states of the confined surface. It is applied to a two-dimensional surface confined within a three-dimensional hypersphere of smaller radius. If the excess surface area is small, the equilibrium states are represented by harmonic deformations of a two-sphere: the ground state is described by a quadrupole; all higher multipoles are shown to be unstable.
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