Recent content by Sasha_Tw

Thank you for your answer! The proof was generalized to higher dimensions, up to ##n=8## by Bray. But my question is about the Huisken and Ilmanen proof. I know there proof was restricted to dimension ##n=3## due to an argument linked to the Geroch monotonicity. I think it is linked to the fact...

I am reading the proof of the Riemannian Penrose Inequality (http://en.wikipedia.org/wiki/Riemannian_Penrose_inequality) by Huisken and Ilmamen in "The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality" and I was wondering why they restrict their proof to the dimension ##n=3##...

Thanks for the response! Concerning the exterior region, is it asymptotically flat ? I am not too familiar with those notions in general but I was reading that for an asymptotically flat manifold, we would have the end of the manifold diffeomorphic to ##\mathbb{R}^3 \setminus K## where ##K## is...

The Schwarzschild spacetime is defined by the following line element \begin{equation*} ds^2 = - \left( 1 - \frac{2m}{r} \right)dt^2 + \frac{1}{1-\frac{2m}{r}}dr^2 + r^2 d\theta^2 + r^2\sin \theta^2 d\phi^2. \end{equation*} We can use the isotropic coordinates, obtained from the Schwarzschild...