Let $(M,g)$ be a compact oriented n-dimensional smooth Riemannian manifold. Consider the following quadratic Riemannian functional$$SR(g) = \int\sb{M}\ \vert R\sb{ijkl}(g)\vert \sp{2}d\mu$$which is homogeneous of degree ...

We present the definitions, derive the relevant Euler-Lagrange equations, and establish various properties concerning biharmonic maps. We investigate several classes of examples exhibiting singular behavior. Existence of ...

Discretizations of self-adjoint, linear, second-order, uniformly elliptic partial differential equations by hybrid mixed finite elements lead to large, ill-conditioned saddle-point problems. By eliminating the flux variable, ...

Let B be a smooth compact orientable surface without boundary and with $\chi(B) < 0.$ We examine two types of fiber bundles M over B with fiber F. The first is a principle fiber bundle with a two-torus fiber and the second ...

We call two closed, oriented 3-manifolds, $M\sb0$ and $M\sb1,$ HTS-equivalent if there exists a sequence $M\sb{j\sb{i}},\ i = 1..m$ where $M\sb0 = M\sb{j\sb1}$ and $M\sb1 = M\sb{j\sb{m}}$ and $M\sb{j\sb{i}}$ is obtained ...

It is shown that the class of quasidisks in the complex plane, with fixed quasicircle constant and area, is compact in both the Hausdorff metric and in the sense of Caratheodory convergence. Compactness for chord-arc domains ...

This thesis discusses the solution of an elliptical conductor problem in two dimensions. This problem can be easily solved in higher dimensions, but in two dimensions, the potential function is logarithmic near infinity. ...

Bryant showed that in a space of constant sectional curvature - c2 (for c &isin; R ), there is a representation for surfaces which have constant mean curvature equal to c, abbreviated as CMC c, which is analogous to ...

We address a classical problem in low dimensional topology: the classification of tamely embedded, finite, connected graphs $G$ in $S\sp3$ up to ambient isotopy. In the case that the graph $G$ is homeomorphic to $S\sp1$, ...

Polyhedral cutting-plane algorithms for hard combinatorial problems have scored notable successes. However, computational research on the Maximum-Weight Cut Problem (MCP) on undirected graphs has been inconclusive. In 1988, ...