By embedding a class of closed Riemannian manifolds (satisfying some curvature assumptions and with diameter bounded from above) into the same Hilbert space, we interpret certain estimates on the heat kernel as giving a precompactness theorem on the class considered.

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In a context where agricultural practices in Europe are likely to go toward extensive systems with lower inputs, it is important to determine the genetic improvement of winter wheat (Triticum aestivum L.) not only in high‐input agricultural systems but also in low‐input systems. This study assesses the improvement in agronomic traits of winter wheat cultivars cultivated in France during the second half of the 20th century at four agronomic treatments: two levels of fungicide were combined with two levels of nitrogen fertilizer. Fourteen cultivars introduced between 1946 and 1992 were grown for two years (1994 and 1995) at five locations. Selection played a major role in the increase in winter wheat yield after 1946. The contribution of selection to this increase depended on the agronomic treatment and varied from one third to one half. Reduction of height was the most important factor. New cultivars with shorter straw expressed higher harvest index values and more consistent higher yields since they were less susceptible to lodging. The ability to produce more kernels from a given total above‐ground biomass was the second factor. The number of kernels per unit area had increased over time without alteration of the weight of the kernels. The negative relationship between 1000‐kernel weight and kernel number/m2 was therefore shifted and new cultivars were thus able to fill more kernels than older entries. Modern cultivars used N more efficiently than their predecessors. The future challenge will be to obtain, in low‐input systems, the same genetic gains as in high‐input systems.

No abstract