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We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies… (More)

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel… (More)

- Mohammad Ghomi
- 2004

The invention provides homogeneous assay methods for nucleic acid hybridization, detection and evaluation. The assay includes obtaining signals from a test sample both before and during the… (More)

Abstract We prove that, in Euclidean space, any nonnegatively curved, compact, smoothly immersed hypersurface lies outside the convex hull of its boundary, provided the boundary satisfies certain… (More)

- Mohammad Ghomi
- 2002

We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.

- Mohammad Ghomi
- 2004

AbstractWe show that the length of any periodic billiard trajectory in
any convex body $$ K \subset \mathbf{R}^n $$
is always at least 4 times the inradius of K; the
equality holds precisely when… (More)

- Mohammad Ghomi
- 2002

A procedure is described for smoothing a convex function which not only preserves its convexity, but also, under suitable conditions, leaves the function unchanged over nearly all the regions where… (More)

Abstract. A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in R3 with a point of positive curvature and no skew loops are the quadrics. In… (More)

- Mohammad Ghomi
- 2006

For a given $n$-dimensional manifold $M^n$ we study the problem of finding the smallest integer $N(M^n$ such that $M^n$ admits a smooth embedding in the Euclidean space $\mathbb{R}^N$ without… (More)

We prove that the area of a hypersurface Σ which traps a given volume outside a convex domain C in Euclidean space Rn is bigger than or equal to the area of a hemisphere which traps the same volume… (More)