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.
A proof of Gauss--Bonnet theorem avoids triangulations using complex structures.
The paper provides an intrinsic proof of a theorem about Landsberg spaces.
In this paper we give a proof of Lichnerowicz Conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the {\it Nice Embeddings} into eigen spaces of the Laplacian. Even if one wants to use these embeddings this paper gives a more streamlined proof.
The paper proves stability of the positive mass theorem using intrinsic flat convergence.
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.
In this expository paper we present short simple proofs of Conway-Gordon-Sachs' theorem on intrinsic linking in three-dimensional space, as well as van Kampen-Flores' and Ummel's theorems on intrinsic intersections. The latter are related to nonrealizability of certain hypergraphs in four-dimensional space. The proofs …
New proof shows no flat embedding for Petersen family graphs.
Proofs Fisher-Rao distance on Gaussian covariance manifold.
Solves Plateau's Problem in Heisenberg group for graphs.
Proves compactness for timed-metric spaces using new distance and maps.
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 …
Normalizes pseudo-Einstein contact forms for easier analysis.
We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-spa…
Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonli…
Study shows DNNs perform well with low intrinsic data dimensions.
PoEL protocol aims to efficiently create and secure liquidity for blockchain networks.
Loi-Piergallini and Akbulut-Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the 2-disk with bounded fibers. In this note we give a more intrinsic alternative proof of this result.
Abstract proof of non-existence of certain types of almost contact metric structures.
The paper proves Rademacher's theorem for Heisenberg groups.
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measu…
We prove general superrigidity results for actions of irreducible lattices on CAT(0) spaces; first, in terms of the ideal boundary, and then for the intrinsic geometry (including for infinite-dimensional spaces). In particular, one obtains a new and self-contained proof of Margulis' superrigidity theorem for uniform ir…
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck…
This paper proves energy convexity for bi-harmonic maps into spheres, with applications to heat flow and uniqueness.
New control on diameter and curvature for evolving surfaces.
We give a new proof of a theorem of Kleiner-Leeb: that any quasi-isometrically embedded Euclidean space in a product of symmetric spaces and Euclidean buildings is contained in a metric neighborhood of finitely many flats, as long as the rank of the Euclidean space is not less than the rank of the target. A bound on th…
Neural network learns to explore and predict actions in a simulated environment.
In this note, we use Chern's magic form in his famous proof of the Gauss-Bonnet theorem to define a mass for asymptotically flat manifolds. It turns out that the new defined mass is equivalent to the one that we introduced recently by using the Gauss-Bonnet-Chern curvature . Moreover, this equivalence implie…
Paper proves uniqueness of Schrödinger flow on specific manifolds.
We provide the proof that the space of time series data is a Kolmogorov space with -separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…
The paper analyzes how much data points can be altered to change their rank in nearest neighbor searches.
We derive and study supergravity BPS flow equations for M5 or D3 branes wrapping a Riemann surface. They take the form of novel geometric flows intrinsically defined on the surface. Their dual field-theoretic interpretation suggests the existence of solutions interpolating between an arbitrary metric in the UV and the …
We present an elementary derivation of the "intrinsic" symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class group $\MCG(S^3,L)$ or $\Sym(L)$ of the pair . Elements in this symmetry group can (and often do) fix the link and act nontrivially onl…
We generalize the "miraculous cancellation" formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruence formulas of Ochanine [O1], Finashin [F] and Zha…
Paper offers a new method for valuing stocks with multiple growth rates.
This expository paper contains a detailed introduction to some important works concerning the Gauss-Bonnet-Chern theorem. The study of this theorem has a long history dating back to Gauss's Theorema Egregium (Latin: Remarkable Theorem) and culminated in Chern's groundbreaking work [14] in 1944, which is a deep and wond…
The paper proves convergence of metrics to a limit in a specific geometric context.
The paper explores how mining costs, rewards, and blockchain security are interconnected.
The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of isometric embeddings of compact surfaces into . We conclude that their proof does not admit a direct extension to higher dimensions. Moreover, we show that, in general, manifolds of dimens…
We give a new proof of a slightly weaker form of a theorem of P. Colmez. This theorem gives a formula for the Faltings height of abelian varieties with complex multiplication by a C.M. field whose Galois group over is abelian; it reduces to the formula of Chowla and Selberg in the case of elliptic curves. We sh…
Proves Goh conditions for singular curves with specific properties.
New proof shows diffusion models implicitly estimate intrinsic dimensionality.
Compactness theorem for timed-metric spaces established.
This paper constructs a function on Gromov-Hausdorff limits of 2-surfaces with curvature constraints.
The study shows properties of stable anisotropic minimal hypersurfaces in 4D space.
New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are…
In this short article, we establish a rigidity theorem for pairs of hyperquadrics in a weaker sense, i.e., we impose a condition that minimal rational curves are preserved, which is stronger than inheriting a sub-VMRT structure, a notion raised by Mok & Zhang (2014). This problem has its source in a theorem of Tsai (19…
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along the lines of the flow interpretation of the Lie bracket. This geometric interpre…