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Local Deformation for Interactive Shape Editing
We introduce a novel regularization for localizing an elastic-energy-driven deformation to only those regions being manipulated by the user. Our local deformation features a natural region of influence, which is automatically adaptive to the geometry...
Matrix Realization of Gauge Theory on Discrete Group $Z_2$
We construct a $2\times 2$ matrix algebra as representation of functions on discrete group $Z_2$ and develop the gauge theory on discrete group proposed by Starz in the matrix algebra. Accordingly, we show that the non-commutative geometry model bu...
I proudly present to you the shive, the physics of the ship with the hitbox of a wave
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Geometric Inequalities on Riemannian and sub-Riemannian manifolds by heat semigroups techn…
In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue University, Institut Henri Poincaré, Levico Summer School and Tata Institut...
Gram Spectrahedra
Representations of nonnegative polynomials as sums of squares are central to real algebraic geometry and the subject of active research. The sum-of-squares representations of a given polynomial are parametrized by the convex body of positive semidefi...
Beurling Nyman Geometry and Gram Matrix Structure, Ladder Density and Polynomial Decay via…
We study the Beurling Nyman (BN) family $f_θ(x) = \{θ/x\} - θ\{1/x\}$ in $L^2((0,1])$ through a multiscale ladder parameterisation $θ_{j,k} = 2^{-j}3^{-k}$ and the associated Gram matrix structure indexed by ladder distance. Using Mellin analysis...
Characterization of some causality conditions through the continuity of the Lorentzian dis…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a non-total impr...
Kissing number - Wikipedia
possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved problems in mathematics In geometry, the kissing number
You've got a Freund--Rubin in Me: The Aretakis Instability of Extremal Black Branes
We investigate how the Aretakis instability affects non-dilatonic extremal black $p$-branes by focusing on their near-horizon geometry. Crucially, the strength of the instability, \textit{i.e.} the number of transverse derivatives needed to see non-d...
NeuralFur: Animal Fur Reconstruction From Multi-View Images
Reconstructing realistic animal fur geometry from images is a challenging task due to the fine-scale details, self-occlusion, and view-dependent appearance of fur. In contrast to human hairstyle reconstruction, there are also no datasets that can be...
Design of an Adaptive Lightweight LiDAR to Decouple Robot-Camera Geometry
A fundamental challenge in robot perception is the coupling of the sensor pose and robot pose. This has led to research in active vision where robot pose is changed to reorient the sensor to areas of interest for perception. Further, egomotion such a...
The History of Barbilian's Metrization Procedure
Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization which is inspired by the study of the models of non-Euclidean geometry. In the present material we discuss the history of Barbilian spaces and the evolut...
Problems for problem session
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry" conference Proce...
real analysis - Why are the rational numbers not continuous ...
Apr 3, 2022 · So you can have continuous functions defined over rationals; but the rationals are not a continuum. Why not? The notion of a continuum has its roots in geometry, and -- in the barest …
Nielsen numbers in topological coincidence theory
We discuss coincidences of pairs (f_1, f_2) of maps between manifolds. We recall briefly the definition of four types of Nielsen numbers which arise naturally from the geometry of generic coincidences. They are lower bounds for the minimum numbers MC...
Junyi42/monst3r
Official Implementation of paper "MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion" (⭐ 1337)
K-contact Lie groups of dimension five or greater
We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the compl...
Geometry of the dephasing sweet spots of spin-orbit qubits
The dephasing time of spin-orbit qubits is limited by the coupling with electrical and charge noise. However, there may exist "dephasing sweet spots" where the qubit decouples (to first order) from the noise so that the dephasing time reaches a maxim...
Naive boundary strata and nilpotent orbits
We study certain real Lie-group orbits in the compact duals of Mumford-Tate domains, verifying a prediction made in [Green, Griffiths, Kerr; Mumford-Tate domains: their geometry and arithmetic] and determining which orbits contain a limit point of so...