Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD209 - 04/21/2015
Alpay, D.; Colombo, F.; Sabadini, I.
Slice Hyperholomorphic Schur Analysis | Abstract | | The purpose of this work is to define and study the counterpart
of Schur functions and Schur analysis in the
slice hyperholomorphic setting. There are at least two
motivations for such a study, both having in the background the desire to replace the complex numbers by the
quaternions. One motivation comes from the theory of linear systems and signal processing. Another motivation is to define new tools and problems in hypercomplex analysis inspired from the complex setting (for instance Nevanlinna-Pick interpolation and the characteristic operator functions).
The monograph is divided in three parts: namely Classical Schur
analysis, Quaternionic analysis, and Quaternionic
Schur analysis. Several parts in the second and third part are original and appear in this work for the first time. |
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QDD208 - 04/20/2015
Catino, G.; Mastrolia, P.; Monticelli, D.D.
A variational characterization of flat spaces in dimension three | Abstract | | In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the sigma_2-curvature functional. |
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QDD207 - 04/20/2015
Catino, G.
On conformally flat manifolds with constant positive scalar curvature | Abstract | | We classify compact conformally flat n-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either S^n with the round metric, S^1×S^{n-1} with the product metric or S^1×S^{n-1} with a rotationally symmetric Derdzinski metric. |
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QDD206 - 04/13/2015
Catino, G.; Mastrolia, P.; Monticelli, D.D.; Rigoli, M.
Analytic and geometric properties of generic Ricci solitons | Abstract | | The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either ????^3, ?×????^2 or ?^3, under some very weak conditions on the vector field X generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the X-Laplacian on every generic Ricci soliton, without any assumption on X. |
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QDD205 - 04/13/2015
Catino, G.
Some rigidity results on critical metrics for quadratic functionals | Abstract | | In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics with unit volume. It is well-known that Einstein metrics are always critical points. The purpose of this article is to show that, under some curvature conditions, a partial converse is true. In particular, for a class of quadratic curvature functionals, we prove that every critical metric with non-negative sectional curvature must be Einstein. |
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QDD204 - 04/08/2015
Catino, G.; Mastrolia, P.; Monticelli, D.D.; Rigoli, M.
Conformal Ricci solitons and related integrability conditions | Abstract | | In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here some necessary integrability conditions for the existence of these structures that also recover, in the corresponding contexts, those already known in the literature for conformally Einstein manifolds and for gradient Ricci solitons. A crucial tool in our analysis is the construction of some appropriate and highly nontrivial (0,3)-tensors related to the geometric structures, that in the special case of gradient Ricci solitons become the celebrated tensor D recently introduced by Cao and Chen. A significant part of our investigation, which has independent interest, is the derivation of a number of commutation rules for covariant derivatives (of functions and tensors) and of transformation laws of some geometric objects under a conformal change of the underlying metric. |
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QDD203 - 04/08/2015
Catino, G.; Mastrolia, P.; Monticelli, D.D.; Rigoli, M.
On the geometry of gradient Einstein-type manifolds | Abstract | | In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold (M,g), unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein manifolds. We show that these general structures can be locally classified when the Bach tensor is null. In particular, we extend a recent result of Cao and Chen. |
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QDD202 - 03/26/2015
Catino, G.; Mantegazza, C.; Mazzieri, L.
Locally Conformally Flat Ancient Ricci Flows | Abstract | | We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature. |
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