Is it true that the resurrected world will be as a sea of glass? Will there be no mountains or valleys?
Two major great changes in the earth will occur in times to come. The first change will occur at the beginning of the Millennium, when the earth will be transformed from a telestial to a terrestrial kingdom. The second great change will come after the millennium when the earth will be transformed from a terrestrial to a celestial kingdom.
In the first transition there will be a major change in the topography of the earth, but it will not become at that time as a sea of glass. We read in the Doctrine and Covenants,
Wherefore, be not deceived, but continue in steadfastness, looking forth for the heavens to be shaken, and the earth to tremble and to reel to and fro as a drunken man, and for the valleys to be exalted, and for the mountains to be made low, and for the rough places to become smooth–and all this when the angel shall sound his trumpet (D&C 49:23).
For the mountains to be made low and the rough places to be made smooth (at the beginning of the millennium) does not mean that the earth will as smooth as a sea of glass. Elder Bruce R. McConkie explains it well, and specifically answers your question about mountains and valleys during the Millennium:
Was this earth once a garden fair, without thorns, thistles, briers, and noxious weeds? It shall be renewed and receive again its Paradisiacal glory. The burning desert shall blossom as the rose and become once again like the garden of the Lord. Was it once blessed with rolling hills, pleasant valleys, and rivers of splendor? In the promised day every mountain shall be made low, every valley shall be exalted, and the rough places shall be made smooth” (Bruce R. McConkie, The Millennial Messiah, p.89).
When the earth is to be changed to a sea of glass is revealed in D&C 77 and further clarified in D&C 130:
Q. What is the sea of glass spoken of by John, 4th chapter, and 6th verse of the Revelation?
A. It is the earth, in its sanctified, immortal, and eternal state (Doctrine and Covenants 77:1).
The angels do not reside on a planet like this earth; But they reside in the presence of God, on a globe like a sea of glass and fire, where all things for their glory are manifest, past, present, and future, and are continually before the Lord (D&C 130:6-7).