Publications related to Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Renormalization of quantum field theory on Riemannian manifolds

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...

2019

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Warped tori with almost non-negative scalar curvature

Davide Parise

For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj = -1j, uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the ...

SPRINGER2019

Detecting Anisotropic Inclusions Through EIT

Jan Cristina

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

Springer2017

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Simultaneous and proportional control of a prosthetic hand and wrist is still a controversial issue, although giant steps have lately been made in this direction. In this paper, we study the application of a novel machine learning method to the problem, wi ...

2017

An Approach for Imitation Learning on Riemannian Manifolds

Sylvain Calinon

In imitation learning, multivariate Gaussians are widely used to encode robot behaviors. Such approaches do not provide the ability to properly represent end-effector orientation, as the distance metric in the space of orientations is not Euclidean. In thi ...

2017

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Nicolas Henri Bernard Flammarion

We consider the minimization of a function deﬁned on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...

2017

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Marc Troyanov

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N ...

Amer Mathematical Soc2017

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

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Renormalization of quantum field theory on Riemannian manifolds

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Warped tori with almost non-negative scalar curvature

Detecting Anisotropic Inclusions Through EIT

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

An Approach for Imitation Learning on Riemannian Manifolds

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Detecting Anisotropic Inclusions Through EIT

Renormalization of quantum field theory on Riemannian manifolds

A vector field method on the distorted Fourier side and decay for wave equations with potentials

The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Warped tori with almost non-negative scalar curvature

An Approach for Imitation Learning on Riemannian Manifolds

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)