By Souza M., Spruck J., Tenenblat K.
We ponder Finsler areas with a Randers metric F = α + β, at the third-dimensional actual vector area, the place α is the Euclidean metric and β is a 1-form with norm b, zero ≤ b < 1. through the use of the thought of suggest curvature for immersions in Finsler areas, brought through Z. Shen, we receive the partial differential equation that characterizes the minimum surfaces that are graphs of capabilities. for every b, zero ≤ b < 1/, we end up that it's an elliptic equation of suggest curvature variety. Then the Bernstein sort theorem and different houses, akin to the nonexistence of remoted singularities, of the strategies of this equation stick with from the speculation developped by way of L. Simon. For b ≥ 1/, the differential equation isn't really elliptic. furthermore, for each b, 1/ < b < 1 we offer options, which describe minimum cones, with an remoted singularity on the foundation.
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Additional info for A Bernstein type theorem on a Randers space
This is not a title) less Dutch and Flemish paintings, whose titles, such as they are, may have come down to us from the anonymous compilers of inventories and auction records, or from the dealers who increasingly circulated that art through Europe in the seventeenth and eighteenth centuries—not to mention the publishers of reproductive prints, whose habit of supplying anecdotal titles for many a Northern genre painting still complicates our reading of these images. But the decline of religious and aristocratic patronage, in which the subject of a work was understood between patron and artist, and the growth of an international art market meant that Italian paintings, too, often acquired their titles from middlemen.
Like the authors of other such documents, the compilers of this catalogue presumably drew in their turn on the language of earlier inventories and on any notations that previous middlemen had marked on the pictures themselves. How they thought of that language is not recorded. But when the Grande Galerie of the Louvre was closed for repairs a few years later, and plans were underway for parts of the collection to hang for the duration in the Salon instead, those charged with organizing the exhibit had also to arrange for a new livret to accompany it.
At the same, however, the history of picture titles also makes clear that with a painting as famous as this one, even an erroneous name will eventually behave like a proper one—which is to say that it will continue to identify the image long after its accuracy has been called into question. As we shall see, once a title has circulated widely enough, the middleman who named the painting after the fact might as well have been present at the baptism. 38 [ 4 • Academie s ] Public arrangements of pictures for display rather than sale became an eighteenth-century phenomenon.
A Bernstein type theorem on a Randers space by Souza M., Spruck J., Tenenblat K.