arXiv research

We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's original proof in the mid-80's, and our purpose here is to assemble these many a…

New proof of homological stability for surface mapping classes.

Simplified proof of stability for Ricci flow near ALE metrics.

A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.

New proof of Minkowski spacetime stability in exterior regions.

New proof of Schwarzschild stability using geometric gauge.

New proof for stability estimates in complex equations without pluripotential theory.

We present a new proof of Reidemeister and Singer's Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound on the minimal genus of a common stabilization in terms of the number of negative slope inflection points and type-two cusps in a Rubinstein-…

We prove effective uniformization for nearly round 2-spheres and investigate their stability.

The paper examines stability of shares in Proof of Stake protocol, identifying different investor behaviors and phase transitions.

The paper proves stability of the positive mass theorem using intrinsic flat convergence.

We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.

Free surface-links are shown to be ribbon links.

We provide a proof of the controlled surgery sequence, including stability, in the special case that the local fundamental groups are trivial. Stability is a key ingredient in the construction of exotic homology manifolds by Bryant, Ferry, Mio and Weinberger, but no proof has been available. The development given here …

In this paper, we discuss stable pairs, which were first studied by S. Paul, and give a proof for a result I learned from him. As a consequence, we will show that the K-stability implies the CM-stability.

We prove that the quotient map from Aut(F_n) to Out(F_n) induces an isomorphism on homology in dimension i for n at least 2i+4. This corrects an earlier proof by the first author and significantly improves the stability range. In the course of the proof, we also prove homology stability for a sequence of groups which a…

Equivalence proven between algebraic stability and geometric stability.

We give another proof of a theorem of Hatcher and Vogtmann stating that the sequence $Aut(F_n)$ satisfies integral homological stability. The paper is for the most part expository, and we also explain Quillen's method for proving homological stability.

Paper proves unbounded stabilization heights of fiber surfaces using Hopf invariant.

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stabili…

We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant and K-stability. It also gives applications concerning the automorphism group.

New proof of Kerr stability outside null cones.

In this paper we present a new proof of the homological stability of the moduli space of closed surfaces in a simply connected background space $K$, which we denote by $S_g (K)$. The homology stability of surfaces in $K$ with an arbitrary number of boundary components, $S_{g,n} (K)$ was studied by the authors in \cite{…

The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.

We correct the proof of Theorem 5 of the paper Homology stability for outer automorphism groups of free groups, by the first two authors.

We annnounce a proof of the fact that a K-stable Fano manifold admits a Kahler-Einstein metric and give a brief outline of the proof.

Simplified proof of equivalence between stability and Bowditch conditions.

New proofs confirm travel time data determine simple metrics on a disc.

New proof of injectivity for broken non-abelian X-ray transform in Minkowski space.

We provide an alternative proof that Crosscaps are diffeomorphically stable.

Paper proves Chow stability implies balanced embedding.

Extends Minkowski stability proof to minimal decay assumptions.

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicia…

Study stability thresholds of big line bundles, proving bounds and generalizing results.

Stable actions of hyperbolic groups on their boundaries.

New proof of stability for expanding Kerr-de Sitter spacetimes with smoothness at the boundary.

New approach proves K-stability of Fano varieties.

We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant…

By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…

Decomposes J-energy into simpler intersection numbers for stability analysis.

We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ for all large $i$.

We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem a…

We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anticanonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that …

Stability of positive mass theorem proven under Ricci curvature bounds.

New theorem shows nearly spherical manifolds can be mapped from spheres.

We give a new proof of Markov's classical theorem relating any two closed braid representations of the same knot or link. The proof is based upon ideas in a forthcoming paper by the authors, "Stabilization in the braid groups". The new proof of the classical Markov theorem is used by Nancy Wrinkle in her forthcoming ma…

Finite p-group actions on manifolds have limited stabilizer subgroups.

We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the general linear groups over the integers and the automorphism groups of free groups.…