Suppose C is a collectionMathworldPlanetmath of mathematical objects (for instance, sets, or functions). Then we say that C is rigid if every cC is uniquely determined by less information about c than one would expect.

It should be emphasized that the above “definition” does not define a mathematical object. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.

Let us illustrate this by some examples:

  1. 1.

    Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.

  2. 2.

    By the fundamental theorem of algebraMathworldPlanetmath, polynomialsMathworldPlanetmathPlanetmathPlanetmath in are rigid in the sense that any polynomial is completely determined by its values on any countably infiniteMathworldPlanetmath set, say , or the unit disk.

  3. 3.

    Linear maps (X,Y) between vector spaces X,Y are rigid in the sense that any L(X,Y) is completely determined by its values on any set of basis vectors of X.

  4. 4.

    Mostow’s rigidity theorem

Title rigid
Canonical name Rigid
Date of creation 2013-03-22 14:38:10
Last modified on 2013-03-22 14:38:10
Owner matte (1858)
Last modified by matte (1858)
Numerical id 11
Author matte (1858)
Entry type Definition
Classification msc 00-01
Synonym rigidity result
Synonym rigidity theorem
Synonym rigidity