What is the physical significance of Mahalanobis distance being less than 1?

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Yvan Dutil

Not, much. Mahalanobis distance is expected to follow a chi2 distribution. Therefore some values below one are expected.

F. Sutaria

For any distribution P(x), defined by a standard deviation s and a mean x0, Mahalanobis distance of any point x in this distribution is |x-x0|/s. Obviously, there will be some values of x for which this will be < 1, and others for which it will be >1.

Ignacio Arroyo-Fernández

My interpretation is that for values you are mentioning, sparsity is exponentially favored. Some images showing lp spaces in the Wikipedia are quite illustrative so far. Unit "balls" are conceived for p >= 1, thus "astroids" do so for 0 < p < 1.

https://en.wikipedia.org/wiki/Lp_space