Search results for "SCALAR"

On the shape of compact hypersurfaces with almost constant mean curvature

2015

The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.

Partial data inverse problems for the Hodge Laplacian

2017

We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…

Manifolds with vectorial torsion

2015

Abstract The present note deals with the properties of metric connections ∇ with vectorial torsion V on semi-Riemannian manifolds ( M n , g ) . We show that the ∇-curvature is symmetric if and only if V ♭ is closed, and that V ⊥ then defines an ( n − 1 ) -dimensional integrable distribution on M n . If the vector field V is exact, we show that the V-curvature coincides up to global rescaling with the Riemannian curvature of a conformally equivalent metric. We prove that it is possible to construct connections with vectorial torsion on warped products of arbitrary dimension matching a given Riemannian or Lorentzian curvature—for example, a V-Ricci-flat connection with vectorial torsion in di…

Bohr radii of vector valued holomorphic functions

2012

Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.

Combinatorics of generalized Bethe equations

2012

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over \({\mathbb{Z}^M}\), and on the other hand, they count integer points in certain M-dimensional polytopes.

A coupled-cluster study of lanthanum trihalide structures

2002

Coupled-cluster calculations were carried at the CCSD(T)-level in order to determine the structures and vibrational spectra of the lanthanum trihalides LaF3 and LaCl3. Two different approaches were employed to describe scalar relativistic effects; the quasi-relativistic Effective Core Potential approach and the all-electron Douglas–Kroll approach. We find LaF3 to be of pyramidal structure and LaCl3 to be planar. The obtained vibrational frequencies accord well with experimental measurements except for the ν2 mode. This disagreement is attributed to the intrinsic uncertainty of harmonic frequencies of this fluxional mode as extracted from spectra which were obtained at high temperature and f…

Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature

1974

Fl�chen Beschr�nkter Mittlerer Kr�mmung in Einer Dreidimensionalen Riemannschen Mannigfaltigkeit

1973

In recent papers HILDEBRANDT [11] and HARTH [5] proved the existence of solutions of the problem of Plateau for surfaces of bounded mean curvature with fixed and free boundaries in E3 and for minimal surfaces with free boundaries in a Riemannian manifold, respectively. Here their methods will be combined to solve the problem of Plateau for surfaces of bounded mean curvature in a Riemannian manifold. This will be done for fixed and free boundaries. Moreover, isoperimetric inequalities for the solutions will be given.

Mean curvature flow of graphs in warped products

2012

Let M be a complete Riemannian manifold which either is compact or has a pole, and let φ be a positive smooth function on M . In the warped product M ×φ R, we study the flow by the mean curvature of a locally Lipschitz continuous graph on M and prove that the flow exists for all time and that the evolving hypersurface is C∞ for t > 0 and is a graph for all t. Moreover, under certain conditions, the flow has a well defined limit.

Volume estimate for a cone with a submanifold as vertex

1992

We give some estimates for the volume of a cone with vertex a submanifold P of a Riemannian or Kaehler manifold M. The estimates are functions of bounds of the mean curvature of P and the sectional curvature of M. They are sharp on cones having a basis which is contained in a tubular hypersurface about P in a space form or in a complex space form.