Equality in the Cauchy-Schwarz and periodic Wirtinger bounds makes the arclength boundary parametrization a first harmonic with orthogonal equal-length coefficient vectors. The boundary is therefore a circle, and the enclosed domain is a disc.

Ancestors (6)

  1. Planar isoperimetric inequality
  2. Euclidean geometry
  3. Geometry and topology
  4. Area of mathematics
  5. Mathematics
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