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An affine isoperimetric inequality.

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The function f(x)=1-2|x|^(1/2) for x in [-1,1]. The natural invariant is rho(y)=1/2(1-y).

A generalized conformal mapping.

A mapping of a domain F:U->U to itself.

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

Let gamma be a path in C, w=f(z), and theta and phi be the tangents to the curves gamma and f(gamma) at z_0 and w_0. If there is an N such that f^((N))(z_0) != 0 (1) ...

A class of area-preserving maps of the form theta_(i+1) = theta_i+2pialpha(r_i) (1) r_(i+1) = r_i, (2) which maps circles into circles but with a twist resulting from the ...

The study of map projections and the making of geographical maps.