177,226 research outputs found
Some geometric properties of hypersurfaces with constant r-mean curvature in euclidean space
No full textLet f : M -> R(m+1) be an isometrically immersed hypersurface. In this paper, we exploit recent results due to the authors to analyze the stability of the differential operator L(r) associated with the rth Newton tensor of f. This appears in the Jacobi operator for the variational problem of minimizing the r-mean curvature H(r). Two natural applications are found. The first one ensures that under a mild condition on the integral of H(r) over geodesic spheres, the Gauss map meets each equator of S(m) infinitely many times. The second one deals with hypersurfaces with zero (r + 1)-mean curvature. Under similar growth assumptions, we prove that the affine tangent spaces f(*)T(p)M, p is an element of M, fill the whole R(m+1)
On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms
No full textAbstractIn this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p−2Du}⩾h(|x|)f(u)±h˜(|x|)ℓ(|Du|), under the main request that h and h˜ are continuous on R+. We achieve our conclusions introducing a generalized version of the well-known Keller–Osserman condition
On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities
No full textIn this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class of p-Laplacian elliptic inequalities with possibly singular weights. In order to get the results a new Omori–Yau type principle is used. We complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite R>0. Finally, a criterium for the existence of positive entire large radial solutions of class is also established
Maps from Riemannian manifolds into non-degenerate Euclidean cones
No full textLet be a connected, non-compact -dimensional Riemannian manifold. In this paper we consider smooth maps with images inside a non-degenerate cone. Under quite general assumptions on , we provide a lower bound for the width of the cone in terms of the energy and the tension of and a metric parameter. As a side product, we recover some well known results concerning harmonic maps, minimal immersions and Kähler submanifolds. In case is an isometric immersion, we also show that, if is sufficiently well-behaved and has non-positive sectional curvature, cannot be contained into a non-degenerate cone of .19 pages, to appea
A note on Killing fields and CMC hypersurfaces
No full textIn this note we give some sufficient conditions for a CMC-hypersurface in a Riemannian manifold N to be invariant under the 1-parameter group of isometries generated by a Killing field on N. Our main result improves on previous ones by D. Hoffman, R. Osserman, and R. Schoen and S. Fornari and J. Ripoll, and hinges on a new, simple existence theorem for a first zero of solutions of an ODE naturally associated to the problem. This theorem implies some classical oscillation criteria of W. Ambrose and R. Moore. Extension to constant higher-order mean curvature hypersurfaces are also presented
Nonlinear weighted p-Laplacian elliptic inequalities with gradient terms
No full textIn this paper, we give sufficient conditions for the existence and nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p-2Du} ≥ h(|x|)f(u)l(|Du|). We achieve our conclusions by using a generalized version of the well-known Keller–Ossermann condition, first introduced in [2] for the generalized mean curvature case, and in [11, Sec. 4] for the nonweighted p-Laplacian equation. Several existence results are also proved in Secs. 2 and 3, from which we deduce simple criteria of independent interest stated in the Introduction
Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights
No full textNon-existence results for non-negative distribution entire solutions of singular quasilinear elliptic differential inequalities with weights are established. Such inequalities include the capillarity equation with varying gravitational field h, as well as the general p-Poisson equation of radiative cooling with varying heat conduction coefficient g and varying radiation coefficient h. Since we deal with inequalities and positive weights, it is not restrictive to assume h radially symmetric. Theorem 1 extends in several directions previous results and says that solely entire large solutions can exist, while Theorem 2 shows that in the p-Laplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest
On the -flow by -Laplace approximation: new estimates via fake distances under Ricci lower bounds
No full textIn this paper we show the existence of weak solutions of the inverse mean curvature flow starting from a relatively
compact set (possibly, a point) on a large class of manifolds satisfying Ricci
lower bounds. Under natural assumptions, we obtain sharp estimates for the
growth of and for the mean curvature of its level sets, that are well
behaved with respect to Gromov-Hausdorff convergence. The construction follows
R. Moser's approximation procedure via the -Laplace equation, and relies on
new gradient and decay estimates for -harmonic capacity potentials, notably
for the kernel of . These bounds, stable as , are achieved by studying fake distances associated to capacity
potentials and Green kernels. We conclude by investigating some basic
isoperimetric properties of the level sets of .Comment: 62 pages, new version. We correct a mistake in our proof of Lemma
2.17. Although we have to strengthen the assumptions therein and,
accordingly, in Theorem 2.22, all of our results on the existence and
properties of the IMCF are not affected. Minor changes, with no influence
elsewhere in the paper, regard Lemma 3.3, Proposition 4.3 and Lemma 5.
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
"Closing the R&D Gap, Evaluating the Sources of R&D Spending"
No full textBoth spending and tax policies have been implemented in the United States with the goal of stimulating private sector research and development (R&D). Karier questions whether current R&D policy, especially the research and experimentation tax credit, can contribute to closing the gap between nondefense expenditures on R&D in the United States and such expenditures in other countries, such as Japan and Germany. He also explores possible changes to our current R&D policy to make it more effective.
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