Saturday, January 19, 2019

Willmore Energy

Any set of discrete quanta of energy, that are spontaneously confined, from within what would here be -- a fully holographic or flat space (a Minkowski-related space, that is to exhibit up to a maximum of 26 spatial dimensions plus time), to where the Ricci Flow of the pertinent topological invariants, that are here to be of such a discrete quantum of energy, may be mathematically described of, as appertaining to the nature relating to:
+ or - ((The mean Gaussian curvature of the surface, that is of the respective cotangent bundle -- that is of such a case)
MINUS (The mean mobius-based curvature of the surface, that is of the respective cotangent bundle -- that is of such a case)).  (+ "out in front," for a Reimman tense of energy, or (- "out in front," for a Nijenhuis tense of energy.)  Generally, this will call for the explication of a Nijenhuis tense of energy.
Here, the said set of discrete quanta of energy, is to spontaneously remain as being of a flat Ricci Curvature, -- to where the said condition of mobiaty, that is of this respective given arbitrary case, is to remain spontaneously superconformally invariant, -- in so long as the correlative Ricci Curvature is to remain flat -- to where the said set of discrete quanta of energy, is to remain as being of a flat space, in so long as there is no external perturbative effect upon the dimensionality of the said set of discrete energy (space-time-fabric that is of a flat Ricci Curvature, is of a purely holographic tense of space) -- that is here in this case, to potentially take upon itself, an approximation of a round-like shape.
Spontaneously means here, that such a case would here to tend to remain as such, in so long as no other non-mentioned factors are to come into play.  Such a set of discrete energy, -- that is to be spontaneously kept as being of a flat space (maximum of 26 spatial dimensions), may be termed of as being here as an example of a "Willmore Energy."  A Willmore Energy, is a manner that is to be taken at a Ward-Cauchy-related level -- by which one is to be able to work at distinguishing the difference between a given actual displayed tense of energy, versus a theoretical completely spherically round tense of energy.  Since I perceive that the space-time-fabric that is of one individually taken set of parallel universes, works to bear a total of 32 spatial dimensions plus time, I have concluded that not all confined spaces are of a flat-space or holographic nature.  Furthermore -- I perceive there are three sets of parallel universes, with one time dimension in common among these, -- since there is only one space-time-continuum.  It then makes sense to me, that Space-Time-Fabric is Volumed space overall.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

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