arXiv subjects

Diego Rodrigues

Publications and source records attributed to Diego Rodrigues.

3 recordsLinked to original sources

arXiv2019

Weighted Alexandrov-Fenchel inequalities in hyperbolic space and a conjecture of Ge, Wang and Wu

We consider a conjecture made by Ge, Wang and Wu regarding weighted Alexandrov-Fenchel inequalities for horospherically convex hypersurfaces in hyperbolic space (a bound, for some physically motivated weight function, of the weighted integral of the $k^{\mathrm{th}}$ mean curvature in terms of the area of the hypersurface). We prove an inequality very similar to the conjectured one. Moreover, when $k$ is zero and the ambient space has dimension three, we give a counterexample to the conjectured inequality.

math.DG↗

arXiv2019

Weighted geometric inequalities for hypersurfaces in sub-static manifolds

We prove two weighted geometric inequalities that hold for strictly mean convex and star-shaped hypersurfaces in Euclidean space. The first one involves the weighted area and the area of the hypersurface and also the volume of the region enclosed by the hypersurface. The second one involves the total weighted mean curvature and the area of the hypersurface. Versions of the first inequality for the sphere and for the adS-Reissner-Nordström manifold are proven. We end with an example of a convex surface for which the ratio between the polar moment of inertia and the square of the area is less than that of the round sphere.

math.DG↗

arXiv2018

A spinorial approach to constant scalar curvature hypersurfaces in pseudo-hyperbolic manifolds

Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.

math.DG↗