Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Share This Author

OPEN PROBLEMS IN GEOMETRY OF CURVES AND SURFACES

- M. Ghomi
- 2017

We collect dozens of well-known and not so well-known fundamental unsolved problems involving low dimensional submanifolds of Euclidean space. The list includes selections from differential geometry,… Expand

62 11- PDF

Circles minimize most knot energies

- Aaron Abrams, Jason H. Cantarella, J. G. Fu, M. Ghomi, R. Howard
- Mathematics
- 16 May 2001

Abstract 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… Expand

61 5- PDF

Optimal Smoothing for Convex Polytopes

- M. Ghomi
- Mathematics
- 1 July 2004

It is proved that given a convex polytope P in R, together with a collection of compact convex subsets in the interior of each facet of P , there exists a smooth convex body arbitrarily close to P… Expand

31 4- PDF

The problem of optimal smoothing for convex functions

- M. Ghomi
- Mathematics
- 25 March 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… Expand

54 4- PDF

Totally skew embeddings of manifolds

- M. Ghomi, S. Tabachnikov
- Mathematics
- 3 July 2003

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… Expand

21 4- PDF

Shortest periodic billiard trajectories in convex bodies

- M. Ghomi
- Mathematics
- 1 April 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… Expand

21 4- PDF

h-Principles for curves and knots of constant curvature

- M. Ghomi
- Mathematics
- 24 July 2007

We prove that $${\mathcal{C}}^\infty$$ curves of constant curvature satisfy, in the sense of Gromov, the relative $${\mathcal{C}}^1$$-dense h-principle in the space of immersed curves in Euclidean… Expand

13 3- PDF

Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature

- M. Ghomi
- Mathematics
- 1 February 2001

We construct smooth closed hypersurfaces of positive curvature with prescribed submanifolds and tangent planes. Further, we develop some applications to boundary value problems via Monge-Amp ere… Expand

47 3- PDF

The relative isoperimetric inequality outside convex domains in Rn

- Jaigyoung Choe, M. Ghomi, M. Ritor'e
- Mathematics
- 27 April 2007

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… Expand

26 2- PDF

The convex hull property and topology of hypersurfaces with nonnegative curvature

- S. Alexander, M. Ghomi
- Mathematics
- 1 December 2003

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… Expand

19 2- PDF

...

1

2

3

4

5

...