On the manifold of closed hypersurfaces in R^n

Abstract

Several results from differential geometry of hypersurfaces in R^n are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the asymptotics of the induced semiflows.

21 pages. To appear

References in corpus (3)

• Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
• On thermodynamically consistent Stefan problems with variable surface energy
• Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension

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• Global existence and full convergence of the Möbius-invariant Willmore flow in the $3$-sphere
• Linearized stability theorem for invariant and quasi-invariant parabolic differential equations in Banach manifolds with applications to free boundary problems
• Real Analytic Solutions to the Willmore Flow
• On the Banach manifold of simple domains in the Euclidean space and applications to free boundary problems
• Qualitative behaviour of incompressible two-phase flows with phase transitions: The case of non-equal densities
• Optimal regularity and exponential stability for the Blackstock-Crighton equation in $L_p$-spaces with Dirichlet and Neumann boundary conditions