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On a compact oriented Finsler manifold without boundary, every cohomology class has a unique harmonic representation. The dimension of the space of all harmonic forms of ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

Let C denote a chain complex, a portion of which is shown below: ...->C_(n+1)->C_n->C_(n-1)->.... Let H_n(C)=kerpartial_n/Impartial_(n+1) denotes the nth homology group. Then ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

A function that has a natural boundary.

Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that ...

One of the Eilenberg-Steenrod axioms. It states that, for every pair (X,A), there is a natural long exact sequence ...->H_n(A)->H_n(X)->H_n(X,A)->H_(n-1)(A)->..., where the ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...