scholarly journals Fisher Vector Coding for Covariance Matrix Descriptors Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

2018 ◽  
Vol 4 (7) ◽  
pp. 85 ◽  
Author(s):  
Ioana Ilea ◽  
Lionel Bombrun ◽  
Salem Said ◽  
Yannick Berthoumieu
Keyword(s):  
Covariance Matrix ◽  
Riemannian Metrics ◽  
Affine Invariant ◽  
Vector Coding ◽  
Fisher Vector ◽  
Invariant Riemannian Metrics

scholarly journals Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups

2013 ◽  
Vol 1 ◽  
pp. 255-275 ◽  
Author(s):  
Luca Capogna ◽  
Giovanna Citti ◽  
Maria Manfredini
Keyword(s):  
Total Variation ◽  
Carnot Group ◽  
Riemannian Metrics ◽  
Heat Kernels ◽  
Gradient Estimates ◽  
Long Time Existence ◽  
Total Variation Flow ◽  
Long Time ◽  
Invariant Riemannian Metrics ◽  
Time Existence

Abstract In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0. The main new contribution are Gaussian-type bounds on the heat kernel for the σε metrics which are stable as ε→0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σε ). We establish interior and boundary gradient estimates, and develop a Schauder theory which are stable as ε → 0. As a consequence we obtain long time existence of smooth solutions of the sub-Riemannian flow (ε = 0), which in turn yield sub-Riemannian minimal surfaces as t → ∞.

scholarly journals On invariant Riemannian metrics on Ledger–Obata spaces

2018 ◽  
Vol 158 (3-4) ◽  
pp. 353-370 ◽  
Author(s):  
Y. Nikolayevsky ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Metrics ◽  
Invariant Riemannian Metrics

scholarly journals Milnor-type theorems for left-invariant Riemannian metrics on Lie groups

2016 ◽  
Vol 68 (2) ◽  
pp. 669-684 ◽  
Author(s):  
Takahiro HASHINAGA ◽  
Hiroshi TAMARU ◽  
Kazuhiro TERADA
Keyword(s):  
Lie Groups ◽  
Riemannian Metrics ◽  
Invariant Riemannian Metrics
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