An ε\varepsilon-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling

In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal bubbles. To this end we replace the total curvature control in T. Rivi\`ere's proof of the $\varepsilon$-regularity for Willmore immersions by a control of the local Willmore energy.Comment: 42 pages, 2 figure

Arts, Culture, and the Social Health of the Nation 2005

Examines the scope and level of participation in arts and culture activities by adults and children, and across income lines, in America. Assesses the value placed on attending arts events and other activities, and barriers that prevent participation

Minimal Bubbling for Willmore Surfaces

In this paper we build an explicit example of a minimal bubble on a Willmore surface, showing there cannot be compactness for Willmore immersions of Willmore energy above $16 \pi$. Additionnally we prove an inequality on the second residue for limits sequences of Willmore immersions with simple minimal bubbles. Doing so, we exclude some gluing configurations and prove compactness for immersed Willmore tori of energy below $12 \pi$.Comment: 51 page

Conformal Gauss Map Geometry and Application to Willmore Surfaces in Model Spaces

In this paper we make a detailed and self-contained study of the conformalGauss map. Then, starting from the seminal work of R. Bryant and the notion of conformal Gauss map, we recover many fundamental properties of Willmore surfaces. We also get new results like some characterizations of minimal and constant meancurvature (CMC) surfaces in term of their conformal Gauss map behavior

A node-wise analysis of the uterine muscle networks for pregnancy monitoring

The recent past years have seen a noticeable increase of interest in the correlation analysis of electrohysterographic (EHG) signals in the perspective of improving the pregnancy monitoring. Here we propose a new approach based on the functional connectivity between multichannel (4x4 matrix) EHG signals recorded from the women abdomen. The proposed pipeline includes i) the computation of the statistical couplings between the multichannel EHG signals, ii) the characterization of the connectivity matrices, computed by using the imaginary part of the coherence, based on the graph-theory analysis and iii) the use of these measures for pregnancy monitoring. The method was evaluated on a dataset of EHGs, in order to track the correlation between EHGs collected by each electrode of the matrix (called node-wise analysis) and follow their evolution along weeks before labor. Results showed that the strength of each node significantly increases from pregnancy to labor. Electrodes located on the median vertical axis of the uterus seemed to be the more discriminant. We speculate that the network-based analysis can be a very promising tool to improve pregnancy monitoring.Comment: 4 pages, 3 figures, accepted in the IEEE EMBC conferanc