@article{BoujemaaYilmazRobicetal.2019,
  author    = {Boujemaa, Hajar and Yilmaz, Alaaddin and Robic, Boris and Koppo, Katrien and Claessen, Guido and Frederix, Ines and Dendale, Paul and V{\"o}ller, Heinz and van Loon, Luc J. C. and Hansen, Dominique},
  title     = {The effect of minimally invasive surgical aortic valve replacement on postoperative pulmonary and skeletal muscle function},
  series = {Experimental physiology},
  volume    = {104},
  journal   = {Experimental physiology},
  number    = {6},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0958-0670},
  doi       = {10.1113/EP087407},
  pages     = {855 -- 865},
  year      = {2019},
  abstract  = {Suboptimal post-operative improvements in functional capacity are often observed after minimally invasive aortic valve replacement (mini-AVR). It remains to be studied how AVR affects the cardiopulmonary and skeletal muscle function during exercise to explain these clinical observations and to provide a basis for improved/tailored post-operative rehabilitation. Twenty two patients with severe aortic stenosis (AS) (aortic valve area (AVA) < 1.0 cm(2)) were preoperatively compared to 22 healthy controls during submaximal constant-workload endurance-type exercise for oxygen uptake (V-O2), carbon dioxide output (V-CO2), respiratory gas exchange ratio, expiratory volume (V-E), ventilatory equivalents for O-2 (V-E/V-O2) and CO2 (V-E/V-CO2), respiratory rate (RR), tidal volume (V-t), heart rate (HR), oxygen pulse (V-O2/HR), blood lactate, Borg ratings of perceived exertion (RPE) and exercise-onset V-O2 kinetics. These exercise tests were repeated at 5 and 21 days after AVR surgery (n = 14), along with echocardiographic examinations. Respiratory exchange ratio and ventilatory equivalents (V-E/V-O2 and V-E/V-CO2) were significantly elevated, V-O2 and V-O2/HR were significantly lowered, and exercise-onset V-O2 kinetics were significantly slower in AS patients vs. healthy controls (P < 0.05). Although the AVA was restored by mini-AVR in AS patients, V-E/V-O2 and V-E/V-CO2 further worsened significantly within 5 days after surgery, accompanied by elevations in Borg RPE, V-E and RR, and lowered V-t. At 21 days after mini-AVR, exercise-onset V-O2 kinetics further slowed significantly (P < 0.05). A decline in pulmonary function was observed early aftermini-AVRsurgery, which was followed by a decline in skeletal muscle function in the subsequent weeks of recovery. Therefore, a tailored rehabilitation programmeshould include training modalities for the respiratory and peripheral muscular system.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2002,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Surgery and the relative index theorem for families of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26300},
  year      = {2002},
  abstract  = {We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Sternin, Boris},
  title     = {Surgery and the relative index in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25538},
  year      = {1999},
  abstract  = {We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin2000,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {On surgery in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25873},
  year      = {2000},
  abstract  = {We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.},
  language  = {en}
}
@article{HermannHumbert2020,
  author    = {Hermann, Andreas and Humbert, Emmanuel},
  title     = {Mass functions of a compact manifold},
  series = {Journal of geometry and physics : JGP},
  volume    = {154},
  journal   = {Journal of geometry and physics : JGP},
  publisher = {Elsevier},
  address   = {Amsterdam [u.a.]},
  issn      = {0393-0440},
  doi       = {10.1016/j.geomphys.2020.103650},
  pages     = {14},
  year      = {2020},
  abstract  = {Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M).},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2001,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Localization problem in index theory of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26175},
  year      = {2001},
  abstract  = {This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.},
  language  = {en}
}