Yes. There are 3 possible shapes of the universe, and these shapes correspond to the theories regarding the end.
Big Crunch corresponds to a spherical universe, a cyclic one.
Big freeze corresponds to a hyperbolic one, which is the least likely due to the derivation of how "flat" the universe is.
Heat death happens due to a flat universe, which the numbers favor by far over the spherical option.
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When you say "flat universe", are you referring to a universe that is literally flat, or one that simply expands in such a manner rather than expanding in a spherical fashion?
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Well obviously we perceive a 4 dimensional system, but the universe is flat in the sense that the energy density is constant everywhere we look.
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Ah so 4 dimensional as in the XYZ axis +time being the 4th?
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Yes, exactly.
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Not sure I follow you. I've studied some astronomy but not that far.