70 citations · 301 across the 32 of their papers we have counts for
7 papers · 1 filter
Deriving Perelman's entropy from Colding's monotonic volume
Ignacio Bustamante, Martin Reiris
In his groundbreaking work from 2002, Perelman introduced two fundamental monotonic quantities: the reduced volume and the entropy. While the reduced volume was motivated by the Bi…
Towards Long-time Geometrization: Stability of the Double-Cusp Spacetimes Under T2-Symmetry
Alejandro Bellati, Martin Reiris
Since the early years of General Relativity, understanding the long-time behavior of the cosmological solutions of Einstein's vacuum equations has been a fundamental yet challengin…
Compact curve shortening flow solutions out of non compact curve
Theodora Bourni, Martin Reiris
We construct a slingshot, that is a compact, embedded solution to curve shortening flow that comes out of a non compact curve and exists for a finite time.
Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Type
Marcus Khuri, Martin Reiris, Gilbert Weinstein +1
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These la…
On Ricci curvature and volume growth in dimension three
Martin Reiris
We prove that any complete metric on R^3 minus a ball with non-negative Ricci curvature and quadratic Ricci-curvature decay, has cubic volume growth.
A note on scalar curvature and the convexity of boundaries
Martin Reiris
We prove that any smooth Riemannian manifold of non-negative scalar curvature and with a strictly mean convex and compact boundary component can be (C^2) extended beyond the compon…
Geometric relations of stable minimal surfaces and applications
Martin Reiris
We establish some a priori geometric relations on stable minimal surfaces lying inside three-manifolds with scalar curvature uniformly bounded below. The relations are based on a s…