Zobrazeno 1 - 10
of 223
pro vyhledávání: '"Ghomi, Mohammad"'
Autor:
Ghomi, Mohammad, Raffaelli, Matteo
We prove that curves of constant torsion satisfy the $C^1$-dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex integrati
Externí odkaz:
http://arxiv.org/abs/2410.06027
Autor:
Ghomi, Mohammad, Raffaelli, Matteo
We prove that curves of constant curvature satisfy the parametric $C^1$-dense relative $h$-principle in the space of immersed curves with nonvanishing curvature in Euclidean space $R^{n\geq 3}$. It follows that two knots of constant curvature in $R^3
Externí odkaz:
http://arxiv.org/abs/2407.01729
Autor:
Ghomi, Mohammad
We show that in Cartan-Hadamard manifolds $M^n$, $n\geq 3$, closed infinitesimally convex hypersurfaces $\Gamma$ bound convex flat regions, if curvature of $M^n$ vanishes on tangent planes of $\Gamma$. This encompasses Chern-Lashof-Sacksteder charact
Externí odkaz:
http://arxiv.org/abs/2308.15454
Autor:
Belegradek, Igor, Ghomi, Mohammad
Using fiber bundle theory and conformal mappings, we continuously select a point from the interior of Jordan domains in Riemannian surfaces. This selection can be made equivariant under isometries, and take on prescribed values such as the center of
Externí odkaz:
http://arxiv.org/abs/2308.03697
Autor:
Ghomi, Mohammad
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel Spruck, which ha
Externí odkaz:
http://arxiv.org/abs/2304.00660
Autor:
Ghomi, Mohammad, Spruck, Joel
We show that a compact Riemannian $3$-manifold $M$ with strictly convex simply connected boundary and sectional curvature $K\leq a\leq 0$ is isometric to a convex domain in a complete simply connected space of constant curvature $a$, provided that $K
Externí odkaz:
http://arxiv.org/abs/2210.05588
Autor:
Ghomi, Mohammad, Wenk, James
We show that in Euclidean 3-space any closed curve $\gamma$ which contains the unit sphere within its convex hull has length $L\geq4\pi$, and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Z
Externí odkaz:
http://arxiv.org/abs/2209.05988
Autor:
Ghomi Mohammad
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 1, Pp 97-102 (2024)
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel Spruck, which ha
Externí odkaz:
https://doaj.org/article/33057ecac62f4d459fb4a58c90dcc088
Autor:
Ghomi, Mohammad, Spruck, Joel
Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. This inequality also improves the known estimates for total mean curvatu
Externí odkaz:
http://arxiv.org/abs/2206.06554
Autor:
Ghomi, Mohammad, Spruck, Joel
We obtain a comparison formula for integrals of mean curvatures of Riemannian hypersurfaces, via Reilly's identities. As applications we derive several geometric inequalities for a convex hypersurface $\Gamma$ in a Cartan-Hadamard manifold $M$. In pa
Externí odkaz:
http://arxiv.org/abs/2204.07624