A5041197817- Nonlinear Partial Differential Equations
- Advanced Mathematical Modeling in Engineering
- Geometric Analysis and Curvature Flows
- Cosmology and Gravitation Theories
- Advanced Differential Geometry Research
- Black Holes and Theoretical Physics
- Geometry and complex manifolds
- Advanced Harmonic Analysis Research
- Differential Equations and Boundary Problems
- Relativity and Gravitational Theory
- Quantum chaos and dynamical systems
- Earth Systems and Cosmic Evolution
- Numerical methods in inverse problems
- Advanced Thermodynamics and Statistical Mechanics
- Galaxies: Formation, Evolution, Phenomena
Pontifical Catholic University of Rio de Janeiro
2019
Universidade de São Paulo
2019
Universidad Central "Marta Abreu" de las Villas (UCLV)
2009-2010
We investigate in detail the asymptotic properties of tachyon cosmology for a broad class self-interaction potentials. The present approach relies on an appropriate re-definition field, which, conjunction with method formerly applied bibliography different context allows us to generalize dynamical systems study wider potentials beyond (inverse) square-law one. It is revealed that independent functional form potential, matter-dominated solution and ultra-relativistic (also matter-dominated)...
We apply the dynamical systems tools to study asymptotic properties of a cosmological model based on non-linear modification General Relativity in which standard Einstein-Hilbert action is replaced by one Dirac-Born-Infeld type. It shown that dynamics this extremely rich: there are found equilibrium points phase space can be associated with matter-dominated, matter-curvature scaling, de Sitter, and even phantom-like solutions. Depending value overall parameters show multi-attractor structure...
The consequences of the constraints which stability de Sitter solutions $f(R)$ theories imposes on Lagrangian's parameters are investigated within metric formalism. It is shown, in particular, that several common Lagrangians do not actually admit matching local with background spaces. Otherwise, asymptotic corresponding models maximally symmetric spaces constant curvature either unstable or anti--de space only stable solution. Additional arguments given favor a previous claim class...
Abstract It is well known that the Serrin condition a necessary for solvability of Dirichlet problem prescribed mean curvature equation in bounded domains $${{\,\mathrm{\mathbb {R}}\,}}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mrow><mml:mspace /><mml:mi>R</mml:mi><mml:mspace /></mml:mrow></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math> with certain regularity. In this paper we investigate sharpness vertical product $$ M^n \times...
These are lecture notes for the mini-course \textit{PDE and hypersurfaces with prescribed mean curvature} held in Federal University of S\~ao Carlos at Workshop on Submanifold Theory Geometric Analysis, August 05 -- 09, 2019. The aim these is to introduce geometers useful tools from \textit{Theory partial differential equations} which used order obtain curvature. For instance, graphs curvature can be obtained by solving Dirichlet problem a particular quasilinear elliptic equation second order.
It is well known that the Serrin condition a necessary for solvability of Dirichlet problem prescribed mean curvature equation in bounded domains $\mathbb{R}^n$ with certain regularity. In this paper we investigate sharpness vertical product $ M^n \times \mathbb{R} $. Precisely, given $\mathscr{C}^2$ domain $\Omega$ $M$ and function H = (x, z) continuous $\overline{\Omega}\times\mathbb{R}$ non-decreasing variable $z$, prove strong $(n-1)\mathcal{H}_{\partial\Omega}(y)\geq...
Given a complete $n$-dimensional Riemannian manifold $M$, we study the existence of vertical graphs in $M\times\mathbb{R}$ with prescribed mean curvature $H=H(x,z)$. Precisely, prove that Dirichlet problem for equation smooth bounded domain $\Omega\subset M$ has solution arbitrary boundary data if $(n-1)\mathcal{H}_{\partial\Omega}(y)\geq n\sup\limits_{z\in\mathbb{R}}\left|{H(y,z)}\right|$ each $y\in\partial\Omega $ provided function $H$ also satisfies $\mathrm{Ricc}_x\geq...
In this work we prove the existence and uniqueness of Killing graphs with prescribed mean curvature considering functions which are not necessarily constant along flow lines vector field.