Blar i Bergen Open Research Archive på forfatter "Grong, Erlend"
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Functional inequalities on path space of sub-Riemannian manifolds and applications
Cheng, Li-Juan; Grong, Erlend; Thalmaier, Anton (Journal article; Peer reviewed, 2021)We consider the path space of a manifold with a measure induced by a stochastic flow with an infinitesimal generator that is hypoelliptic, but not elliptic. These generators can be seen as sub-Laplacians of a sub-Riemannian ... -
Geometric rough paths on infinite dimensional spaces
Grong, Erlend; Nilssen, Torstein; Schmeding, Alexander (Journal article; Peer reviewed, 2022)Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For α ∈ (1/3,1/2), we give criteria for when we can approximate Banach space-valued ... -
H-type foliations
Baudoin, Fabrice; Grong, Erlend; Rizzi, Luca; Vega-Molino, Gianmarco (Journal article; Peer reviewed, 2022)With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, ... -
A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations
Baudoin, Fabrice; Grong, Erlend; Vega-Molino, Gianmarco (Journal article; Peer reviewed, 2022)Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian ... -
Horizontal holonomy and foliated manifolds
Chitour, Yacine; Grong, Erlend; Jean, Frederic; Kokkonen, Petri (Journal article; Peer reviewed, 2019)We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle D of the tangent bundle. We provide explicit means of computing these holonomy groups ... -
Matching univalent functions and related problems of conformal mappings
Grong, Erlend (Master thesis, 2008) -
Nonholonomic geometry on finite and infinite dimensional Lie groups and rolling manifolds
Grong, Erlend (Doctoral thesis, 2012-03-30)Part I: We start by giving some background on the topics discussed in this thesis. The main topic of the thesis is nonholonomic geometry. In Chapter 1 we give an introduction of nonholonomic geometry in the context of ... -
Radial processes for sub-Riemannian Brownian motions and applications
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa; Neel, Robert; Thalmaier, Anton (Journal article; Peer reviewed, 2020)We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô’s formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian ...