A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New proof of Willmore inequality using geometric divergence inequality.
First geometric proof of the flyping theorem.
New geometric proof of convex function differentiability and approximation.
Introduces a new canonical connection for Riemannian manifolds and proves Frobenius theorem geometrically.
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 give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
Geometrically constructs dilogarithm from Chern-Simons theory.
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
This paper has been withdrawn by the author due a crucial sign error in Theorem B. We present a geometric proof of Thom conjecture, which uses Khovanov homology. Our approach doesn't use any analytic methods and is quite different from proof given by Kronheimer and Mrowka in 1994.
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the ori…
We give a proof that the geometric K-homology theory for finite CW-complexes defined by Baum and Douglas is isomorphic to Kasparov's K-homology. The proof is a simplification of more elaborate arguments which deal with the geometric formulation of equivariant K-homology theory.
New geometric proof for rational tangles links-quivers correspondence.
Transformed geometry into algebra to prove Pick's theorem efficiently.
Geometric proof of contractibility of unitary group in strong topology.
New proofs for complex Hopf manifolds using geometric structures.
In this note we give geometric formulations and proofs of three results of S. Morita. These results relate certain two dimensional cohomology classes of various moduli spaces of curves. We also give a geometric interpretation of a fourth result of Morita. One motivation of this work is to facilitate the application of …
Proof shows cones minimize certain geometric functionals.
We give a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations including the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman…
Simplified proof of spin^c structures using twistor spaces.
In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit. In fact, this is equivalent to a well-known result of Mostow about existence of compatible Cartan decompositions.
Summary of tensor tomography proofs on manifolds with boundaries.
Geometric approach to moment maps in complex geometry.
Proof shows volumes of certain geometric representations are always integers.
Two new proofs classify complete totally geodesic subsets of complex hyperbolic plane.
A new simple proof for surface map degree inequality.
In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In particular, we give a detailed exposition of a complete proof of the Poincaré con…
New proof confirms rolling objects can follow any path.
New proof and description of commutator subgroups for free and surface groups.
Constructs knots from 3-manifolds with specified geometric limits.
New weighted geometric inequalities for hypersurfaces in R^n proved.
Proof of reverse isoperimetric inequality for black holes.
We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary to curves without boundary. Our method is new and geometric and…
New proof of Schwarzschild stability using geometric gauge.
We give a new proof of the fact that the condition of a Fano manifold admitting a Kähler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability. The arguments involve estimates of Futaki invariants obtained from a differential…
The Whitney-Graustein theorem states that regular closed curves in the 2-plane are classified, up to regular homotopy, by their rotation number. Here we give a simple proof based on contact geometry.
We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.
New proof finds three divergence-free vector fields for any 3D manifold.
An elementary proof shows that quasi-isometric groups to integers are virtually integers.
The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.
We give a unified geometric approach to some theorems about primitive elements and palindromes in free groups of rank 2. The geometric treatment gives new proofs of the theorems. Dedicated to Bill Harvey on his 65th birthday.
Direct proof of hyperbolicity for a family of knots.
We prove a partial generalization of Bonahon's tameness result to surfaces inside irreducible 3-manifolds with hyperbolic fundamental group. Bonahon's result states that geometrically infinite ends of freely indecomposable hyperbolic 3-manifolds are simply degenerate. It is easy to see that a geometrically infinite end…
Proof of local well-posedness for a specific boundary condition in general relativity.
New geometric proof shows index of umbilic points on analytic surfaces is at most one.
Unified proof of Teichmüller components using robust submanifolds.
We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and …
Simplified proof of K3 surface period map surjectivity.