Search results for "scalar [resonance]"
showing 10 items of 45 documents
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.
Curvature locus and principal configurations of submanifolds of Euclidean space
2017
We study relations between the properties of the curvature loci of a submanifold M in Euclidean space and the behaviour of the principal configurations of M, in particular the existence of umbilic and quasiumbilic fields. We pay special attention to the case of submanifolds with vanishing normal curvature. We also characterize local convexity in terms of the curvature locus position in the normal space.
Multiplicity of ground states for the scalar curvature equation
2019
We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…
Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry
2022
AbstractWe study existence and multiplicity of positive ground states for the scalar curvature equation $$\begin{aligned} \varDelta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n\,, \quad n>2, \end{aligned}$$ Δ u + K ( | x | ) u n + 2 n - 2 = 0 , x ∈ R n , n > 2 , when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ K : R + → R + is bounded above and below by two positive constants, i.e. $$0<\underline{K} \le K(r) \le \overline{K}$$ 0 < K ̲ ≤ K ( r ) ≤ K ¯ for every $$r > 0$$ r > 0 , it is decreasing in $$(0,{{{\mathcal {R}}}})$$ ( 0 , R ) and increasing in $$({{{\mathcal {R}}}},+\infty )$$ ( R , + ∞ ) for a certain $${{{\mathcal {R}}}}&g…
Normal Coulomb Frames in $${\mathbb{R}}^{4}$$
2012
Now we consider two-dimensional surfaces immersed in Euclidean spaces \({\mathbb{R}}^{n+2}\) of arbitrary dimension. The construction of normal Coulomb frames turns out to be more intricate and requires a profound analysis of nonlinear elliptic systems in two variables. The Euler–Lagrange equations of the functional of total torsion are identified as non-linear elliptic systems with quadratic growth in the gradient, and, more exactly, the nonlinearity in the gradient is of so-called curl-type, while the Euler–Lagrange equations appear in a div-curl-form. We discuss the interplay between curvatures of the normal bundles and torsion properties of normal Coulomb frames. It turns out that such …
Charmed hadrons in nuclear medium
2010
5th International Conference on Quarks and Nuclear Physics (QNP09).Inst High Energy Phys Chinese Acad Sci, Beijing, PEOPLES R CHINA, SEP 21-25, 2009
Zero-field nuclear magnetic resonance spectroscopy of viscous liquids
2014
Abstract We report zero-field NMR measurements of a viscous organic liquid, ethylene glycol. Zero-field spectra were taken showing resolved scalar spin–spin coupling (J-coupling) for ethylene glycol at different temperatures and water contents. Molecular dynamics strongly affects the resonance linewidth, which closely follows viscosity. Quantum chemical calculations have been used to obtain the relative stability and coupling constants of all ethylene glycol conformers. The results show the potential of zero-field NMR as a probe of molecular structure and dynamics in a wide range of environments, including viscous fluids.
Dynamical Aspects of Generalized Palatini Theories of Gravity
2009
We study the field equations of modified theories of gravity in which the Lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the Levi-Civitagrave connection of an auxiliary metric which, in particular cases of interest, is related with the physical metric by means of a disformal transformation. This relation between physical and auxiliary metric boils down to a conformal transformation in the case of f(R) theories. We also show with explicit models that the inclusion of Ricci-squared terms in the action can impose upper bounds on the accessible values of pressure and density, which m…