How can I match characters (with the intention of removing them) from outside the unicode Basic Multilingual Plane in java?
To remove all non-BMP characters, the following should work:
String sanitizedString = inputString.replaceAll("[^\u0000-\uFFFF]", "");
                        Are you looking for specific characters or all characters outside the BMP?
If the former, you can use a StringBuilder to construct a string containing code points from the higher planes, and regex will work as expected:
  String test = new StringBuilder().append("test").appendCodePoint(0x10300).append("test").toString();
  Pattern regex = Pattern.compile(new StringBuilder().appendCodePoint(0x10300).toString());
  Matcher matcher = regex.matcher(test);
  matcher.find();
  System.out.println(matcher.start());
If you're looking to remove all non-BMP characters from a string, then I'd use StringBuilder directly rather than regex:
  StringBuilder sb = new StringBuilder(test.length());
  for (int ii = 0 ; ii < test.length() ; )
  {
     int codePoint = test.codePointAt(ii);
     if (codePoint > 0xFFFF)
     {
        ii += Character.charCount(codePoint);
     }
     else
     {
        sb.appendCodePoint(codePoint);
        ii++;
     }
  }
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