What are other peoples minds according to the Laṅkāvatāra Sūtra? I read that everything is just my own mind from the Laṅkāvatāra Sūtra. If everything is my own mind, what about other peoples minds? Are they also my own mind? How can this be understood?

For instance in Chapter 7 of the Laṅkāvatāra Sūtra there is this passage:


  The Blessed One replied: There are four things by the fulfilling of
  which an earnest disciple may gain self-realization of Noble Wisdom
  and become and Bodhisattva-Mahasattva: First, he must have a clear
  understanding that all things are only manifestations of the mind
  itself; second, he must discard the notion of birth, abiding and
  disappearance; third, he must clearly understand the ego-less-ness of
  both things and persons; and fourth, he must have a true conception of
  what constitutes self-realization of Noble Wisdom, provided with these
  four understandings, earnest disciples may become Bodhisattvas and
  attain Transcendental Intelligence.


If all things are manifestations of my own mind, doesn't this mean Buddhism as expressed in this Sutra is the equivalent of solipsism? How do we understand the problem of other minds given this Sutra?
Thrangu Rinpoche once said that everything we see (all phenomena we experience) is our own projection - except other people's minds. Only other people's subjective experience is not our projection and therefore exists independently of us.