Geometric Problems

1976 ◽  
pp. 157-162
Author(s):  
George Pólya ◽  
Gabor Szegö
Keyword(s):  
Geometric Problems

The Book Review Column1

2021 ◽  
Vol 51 (4) ◽  
pp. 4-5
Author(s):  
Frederic Green
Keyword(s):  
Parameterized Complexity ◽  
Property Testing ◽  
The Third ◽  
Geometric Problems ◽  
The Subject

The three books reviewed in this column are about central ideas in algorithms, complexity, and geometry. The third one brings together topics from the first two by applying techniques of both property testing (the subject of the first book) and parameterized complexity (including its more focused incarnation studied in the second book, kernelization) to geometric problems.

Geometric Problems in Automated Manufacturing

OPSEARCH ◽  
1999 ◽  
Vol 36 (1) ◽  
pp. 42-50
Author(s):  
R. Chandrasekaran ◽  
Santosh N. Kabadi
Keyword(s):  
Automated Manufacturing ◽  
Geometric Problems

Some geometric problems connected with hyperbolic capacity

1977 ◽  
Vol 8 (6) ◽  
pp. 662-704
Author(s):  
G. V. Kuz'mina
Keyword(s):  
Geometric Problems ◽  
Hyperbolic Capacity

Geometric Problems

1976 ◽  
pp. 366-379
Author(s):  
George Pólya ◽  
Gabor Szegö
Keyword(s):  
Geometric Problems

scholarly journals Geometric Problems with Application to Hashing

1982 ◽  
Vol 11 (2) ◽  
pp. 217-226 ◽  
Author(s):  
Douglas Comer ◽  
Michael J. O’Donnell
Keyword(s):  
Geometric Problems

scholarly journals Generic Dynamical Properties of Connections on Vector Bundles

2021 ◽  
Author(s):  
Mihajlo Cekić ◽  
Thibault Lefeuvre
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Differential Operators ◽  
Parallel Transport ◽  
Conformal Killing ◽  
Generic Properties ◽  
Geometric Problems ◽  
Pseudo Differential Operators ◽  
Divergence Type ◽  
Open Question

Abstract Given a smooth Hermitian vector bundle $\mathcal{E}$ over a closed Riemannian manifold $(M,g)$, we study generic properties of unitary connections $\nabla ^{\mathcal{E}}$ on the vector bundle $\mathcal{E}$. First of all, we show that twisted conformal Killing tensors (CKTs) are generically trivial when $\dim (M) \geq 3$, answering an open question of Guillarmou–Paternain–Salo–Uhlmann [ 14]. In negative curvature, it is known that the existence of twisted CKTs is the only obstruction to solving exactly the twisted cohomological equations, which may appear in various geometric problems such as the study of transparent connections. The main result of this paper says that these equations can be generically solved. As a by-product, we also obtain that the induced connection $\nabla ^{\textrm{End}({\operatorname{{\mathcal{E}}}})}$ on the endomorphism bundle $\textrm{End}({\operatorname{{\mathcal{E}}}})$ has generically trivial CKTs as long as $(M,g)$ has no nontrivial CKTs on its trivial line bundle. Eventually, we show that, under the additional assumption that $(M,g)$ is Anosov (i.e., the geodesic flow is Anosov on the unit tangent bundle), the connections are generically opaque, namely that generically there are no non-trivial subbundles of $\mathcal{E}$ that are preserved by parallel transport along geodesics. The proofs rely on the introduction of a new microlocal property for (pseudo)differential operators called operators of uniform divergence type, and on perturbative arguments from spectral theory (especially on the theory of Pollicott–Ruelle resonances in the Anosov case).

Sign in / Sign up

Export Citation Format

Share Document