arXiv research

Recalls intrinsically harmonic forms and open problems.

A note on setting swap parameters for traders.

Short note finds a new metric from sphere quotients.

It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in ge…

Short note shows unbounded dimensions in Fano K-moduli spaces.

In this short note we discuss some recent results about two-positive Ricci curvature and their applications to positive Einstein curvature.

The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.

Authors compute fundamental groups for a specific topological group.

Huisken's isoperimetric mass is always nonnegative.

In this short note, we show that the assumption "convex" in Theorem 7 of Brendle-Eichmair's paper \cite{BE} is unnecessary.

In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.

In this short note it is established that there does not exist Ricci soliton with the Reeb potential vector field in an almost Kenmotsu manifold (briefly, $\mathcal{AKM}$).

Short note on braid index and quasipositivity of certain pretzel knots.

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.

In this short note, we exhibit an infinite family of hyperbolic rational homology $3$--spheres which do not admit any fillable contact structures. We also note that most of these manifolds do admit tight contact structures.

Short note on soft-max and policy gradients in bandit problems using Lyapunov functions.

Geodesically convex functions are continuous on Riemannian manifolds.

Short note on upper bounds for loop homology classes.

In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.

By the curve shortening flow, the only closed embedded contracting self-similar solutions are circles: we give a very short and intuitive geometric proof of this basic and classical result using an idea of Gage.

In this short note we show the existence of an epimorphism between groups of $2$-bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of $2$-bridge knots by Riley polynomials.

In this note we present a short proof that the 4 oriented Reidemeister moves of type 2 together with any one of the 8 oriented Reidemeister moves of type 3 are sufficient to imply the other 7.

In this short note, we give simple proof of the Ricci flow's local existence and uniqueness on closed Einstein manifolds. We suggest a new setting for studying the space of Riemannian metrics on a compact manifold.

This is a short expository note about Calabi-Yau manifolds and degenerations of their Ricci-flat metrics.

In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.

Short proof given for a complex formula in spin manifold geometry.

In this note, we prove an existence result on exhaustion functions adapting the method by L.-F. Tam. Then we apply it to prove short-time existence of Ricci flow and study Yau's uniformization conjecture using similar method as Fei He and Lee-Tam.

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.

Improves bounds on surface decompositions.

Short note observes quantum Hochschild homology as a composition of known operations.

In this note we consider 2-step nilpotent Lie algebras associated with graphs. We prove that 2-step nilpotent Lie algebras $\n$ and $\n'$ associated with graphs $(S, E)$ and $(S', E')$ respectively are isomorphic if and only if $(S, E)$ and $(S', E')$ are isomorphic.

In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.

Short introduction to discrete flat fronts in hyperbolic space with a Weierstrass representation proof.

In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.

In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.

Note on subgaussian bounds for sign-quantized linear maps.

In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

Notes a flaw in a proof about embedding graphs.

In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This theorem was first proved by F. Ledrappier and X. Wang in [1].

In this short note we apply methods introduced by B. Hanke and T. Shick to prove the vanishing of (low dimensional) higher $A$-genera for spin manifolds admitting a positive scalar curvature metric. Our aim is to provide a short and unified proof for this beautiful result without using the strong Novikov conjecture.

In this short note, we show that homogeneous Ricci solitons are algebraic. As an application, we see that the generalized Alekseevskii conjecture is equivalent to the Alekseevskii conjecture.

In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.

In this short note, we prove the Miyaoka-Yau inequality for minimal projective $n$-manifolds of general type by using Kähler-Ricci flow.

In this short note, we will show how to optimize the portfolio of a large trader whose hedging strategy affects the price of his assets.

Explains how to prove positive mass theorem with boundary in dimensions less than 8.

In this short note we show how the higher index theory can be used to prove results concerning the non-existence of complete riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods in dealing with …