Linked from

The 19 pages that link to Isoperimetric inequality, each with the reason it gives.

• PerimeterRelated: It relates the maximum enclosed area to a fixed boundary length.

• Surface-area-to-volume ratioRelated: It shows that shape changes the ratio even when volume stays fixed.

• Equality conditionRelated: Equality singles out extremal shapes, such as the circle in the planar case.

• Geometric inequalityBroader topic: It gives a canonical sharp relation between boundary length and enclosed area.

• Isoperimetric problemCompared with: The inequality states a global bound; the problem asks for the extremizer attaining it.

• Convex bodyRelated: Convex bodies provide a central setting for sharp volume–surface comparisons.

• Cavalieri's principleCompared with: It compares global boundary and volume measures, not level-by-level cross-sections.

• Sobolev inequalityRelated: Geometric isoperimetric bounds provide a route to classical Sobolev inequalities.

• Weitzenböck's inequalityRelated: It shares the theme of bounding area from boundary measurements, though its sharp shape differs.

• Barbier's theoremCompared with: Unlike Barbier's equality for constant width, it compares area and perimeter across all plane regions.

• Crofton formulaCompared with: It constrains length through area rather than reconstructing length from intersection counts.

• Hadwiger–Finsler inequalityNarrower topic: This triangle inequality is a sharp area bound within the broader isoperimetric tradition.

• Pedoe's inequalityRelated: Both results constrain area using measurements of a boundary, though Pedoe compares two triangles.

• Brunn–Minkowski theoremRelated: Brunn–Minkowski provides a route to classical bounds on boundary area and volume.

• Cartan–Hadamard conjectureRelated: Sharp volume lower bounds interact with geometric questions about boundary area and enclosed volume.

• Dittert conjectureRelated: The conjecture is a simplex-extremal problem under fixed volume, akin to isoperimetric questions.

• Double bubble theoremCompared with: It treats one enclosed region, whereas the double bubble theorem treats two regions sharing a boundary.

• Filling area conjectureRelated: Like isoperimetric inequalities, it bounds area using boundary data, but fixes intrinsic distances.

• Honeycomb theoremRelated: Its area–perimeter bound helps control the shapes of individual cells.